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run

Definitions

  • "Three men came running up."
    "Three men came running up."
  • WordNet 3.6
    • v run become undone "the sweater unraveled"
    • v run come unraveled or undone as if by snagging "Her nylons were running"
    • v run reduce or cause to be reduced from a solid to a liquid state, usually by heating "melt butter","melt down gold","The wax melted in the sun"
    • v run cause to perform "run a subject","run a process"
    • v run progress by being changed "The speech has to go through several more drafts","run through your presentation before the meeting"
    • v run change from one state to another "run amok","run rogue","run riot"
    • v run compete in a race "he is running the Marathon this year","let's race and see who gets there first"
    • v run run, stand, or compete for an office or a position "Who's running for treasurer this year?"
    • v run pursue for food or sport (as of wild animals) "Goering often hunted wild boars in Poland","The dogs are running deer","The Duke hunted in these woods"
    • v run pass over, across, or through "He ran his eyes over her body","She ran her fingers along the carved figurine","He drew her hair through his fingers"
    • v run perform as expected when applied "The washing machine won't go unless it's plugged in","Does this old car still run well?","This old radio doesn't work anymore"
    • v run be operating, running or functioning "The car is still running--turn it off!"
    • v run carry out "run an errand"
    • v run cause to emit recorded audio or video "They ran the tapes over and over again","I'll play you my favorite record","He never tires of playing that video"
    • v run include as the content; broadcast or publicize "We ran the ad three times","This paper carries a restaurant review","All major networks carried the press conference"
    • v run travel a route regularly "Ships ply the waters near the coast"
    • v run cover by running; run a certain distance "She ran 10 miles that day"
    • v run move fast by using one's feet, with one foot off the ground at any given time "Don't run--you'll be out of breath","The children ran to the store"
    • v run travel rapidly, by any (unspecified) means "Run to the store!","She always runs to Italy, because she has a lover there"
    • v run run with the ball; in such sports as football
    • v run keep company "the heifers run with the bulls to produce offspring"
    • v run sail before the wind
    • v run be diffused "These dyes and colors are guaranteed not to run"
    • v run move along, of liquids "Water flowed into the cave","the Missouri feeds into the Mississippi"
    • v run flee; take to one's heels; cut and run "If you see this man, run!","The burglars escaped before the police showed up"
    • v run cause an animal to move fast "run the dogs"
    • v run move about freely and without restraint, or act as if running around in an uncontrolled way "who are these people running around in the building?","She runs around telling everyone of her troubles","let the dogs run free"
    • v run deal in illegally, such as arms or liquor
    • v run set animals loose to graze
    • v run direct or control; projects, businesses, etc. "She is running a relief operation in the Sudan"
    • v run make without a miss
    • v run carry out a process or program, as on a computer or a machine "Run the dishwasher","run a new program on the Mac","the computer executed the instruction"
    • v run occur persistently "Musical talent runs in the family"
    • v run continue to exist "These stories die hard","The legend of Elvis endures"
    • v run extend or continue for a certain period of time "The film runs 5 hours"
    • v run stretch out over a distance, space, time, or scope; run or extend between two points or beyond a certain point "Service runs all the way to Cranbury","His knowledge doesn't go very far","My memory extends back to my fourth year of life","The facts extend beyond a consideration of her personal assets"
    • v run cause something to pass or lead somewhere "Run the wire behind the cabinet"
    • v run have a tendency or disposition to do or be something; be inclined "She tends to be nervous before her lectures","These dresses run small","He inclined to corpulence"
    • v run be affected by; be subjected to "run a temperature","run a risk"
    • v run have a particular form "the story or argument runs as follows","as the saying goes..."
    • v run change or be different within limits "Estimates for the losses in the earthquake range as high as $2 billion","Interest rates run from 5 to 10 percent","The instruments ranged from tuba to cymbals","My students range from very bright to dull"
    • n run a score in baseball made by a runner touching all four bases safely "the Yankees scored 3 runs in the bottom of the 9th","their first tally came in the 3rd inning"
    • n run the act of running; traveling on foot at a fast pace "he broke into a run","his daily run keeps him fit"
    • n run a regular trip "the ship made its run in record time"
    • n run a short trip "take a run into town"
    • n run (American football) a play in which a player attempts to carry the ball through or past the opposing team "the defensive line braced to stop the run","the coach put great emphasis on running"
    • n run the act of testing something "in the experimental trials the amount of carbon was measured separately","he called each flip of the coin a new trial"
    • n run an unbroken chronological sequence "the play had a long run on Broadway","the team enjoyed a brief run of victories"
    • n run the pouring forth of a fluid
    • n run a row of unravelled stitches "she got a run in her stocking"
    • n run a race run on foot "she broke the record for the half-mile run"
    • n run a race between candidates for elective office "I managed his campaign for governor","he is raising money for a Senate run"
    • n run an unbroken series of events "had a streak of bad luck","Nicklaus had a run of birdies"
    • n run a small stream
    • n run the production achieved during a continuous period of operation (of a machine or factory etc.) "a daily run of 100,000 gallons of paint"
    • n run unrestricted freedom to use "he has the run of the house"
    • n run the continuous period of time during which something (a machine or a factory) operates or continues in operation "the assembly line was on a 12-hour run"
    • ***

Additional illustrations & photos:

Ye Olde Running Horse Inn, Leatherhead Ye Olde Running Horse Inn, Leatherhead
VIEW OF THE "COUNTRY" THROUGH WHICH THE RAILWAY RUNS VIEW OF THE "COUNTRY" THROUGH WHICH THE RAILWAY RUNS
Running Running
Running Noose Running Noose
Crossed Running Noose Crossed Running Noose
Sam White's run Sam White's run
The witch and the wolf running The witch and the wolf running
Rosenbaum Runs Into Sigel's Pickets. 66 Rosenbaum Runs Into Sigel's Pickets. 66

Webster's Revised Unabridged Dictionary
  • Interesting fact: Wild turkeys can run at speeds of up to 25 miles per hour
    • Run A continuing urgent demand; especially, a pressure on a bank or treasury for payment of its notes.
    • Run A course; a series; that which continues in a certain course or series; as, a run of good or bad luck. "They who made their arrangements in the first run of misadventure . . . put a seal on their calamities."
    • Run (Piquet, Cribbage, etc) A number of cards of the same suit in sequence; as, a run of four in hearts.
    • Run A pair or set of millstones.
    • Run A pleasure excursion; a trip. "I think of giving her a run in London."
    • Run A range or extent of ground for feeding stock; as, a sheep run .
    • Run (Mus) A roulade, or series of running tones.
    • Run A small stream; a brook; a creek.
    • Run (Naut) A voyage; as, a run to China.
    • Run Continued repetition on the stage; -- said of a play; as, to have a run of a hundred successive nights. "A canting, mawkish play . . . had an immense run ."
    • Run (Sport) In baseball, a complete circuit of the bases made by a player, which enables him to score one point; also, the point thus scored; in cricket, a passing from one wicket to the other, by which one point is scored; as, a player made three runs; the side went out with two hundred runs; the Yankees scored three runs in the seventh inning. "The “ runs ” are made from wicket to wicket, the batsmen interchanging ends at each run ."
    • Run Melted, or made from molten material; cast in a mold; as, run butter; run iron or lead.
    • Run Smuggled; as, run goods.
    • Run Specifically, of a horse: To move rapidly in a gait in which each leg acts in turn as a propeller and a supporter, and in which for an instant all the limbs are gathered in the air under the body.
    • Run State of being current; currency; popularity. "It is impossible for detached papers to have a general run, or long continuance, if not diversified with humor."
    • Run That which runs or flows in the course of a certain operation, or during a certain time; as, a run of must in wine making; the first run of sap in a maple orchard.
    • Run The act of migrating, or ascending a river to spawn; -- said of fish; also, an assemblage or school of fishes which migrate, or ascend a river for the purpose of spawning.
    • Run The act of running; as, a long run; a good run; a quick run; to go on the run .
    • Run (Naut) The aftermost part of a vessel's hull where it narrows toward the stern, under the quarter.
    • Run (Golf) The distance a ball travels after touching the ground from a stroke.
    • Run (Naut) The distance sailed by a ship; as, a good run; a run of fifty miles.
    • Run (Mil) The greatest degree of swiftness in marching. It is executed upon the same principles as the double-quick, but with greater speed.
    • Run (Mining) The horizontal distance to which a drift may be carried, either by license of the proprietor of a mine or by the nature of the formation; also, the direction which a vein of ore or other substance takes.
    • Run (Golf) The movement communicated to a golf ball by running.
    • Run To be charged with, or to contain much of, while flowing; as, the rivers ran blood.
    • Run To be in form thus, as a combination of words.
    • run to be on the same footing; to correspond (with) exactly; to be alike in all the circumstances to be considered.
    • Run To be played on the stage a number of successive days or nights; as, the piece ran for six months.
    • Run To be popularly known; to be generally received.
    • Run To become fluid; to melt; to fuse.
    • Run To cause to be drawn; to mark out; to indicate; to determine; as, to run a line.
    • Run To cause to enter; to thrust; as, to run a sword into or through the body; to run a nail into the foot. "You run your head into the lion's mouth.""Having run his fingers through his hair."
    • Run To cause to pass, or evade, offical restrictions; to smuggle; -- said of contraband or dutiable goods. "Heavy impositions . . . are a strong temptation of running goods."
    • Run To cause to run (in the various senses of Run v. i.); as, to run a horse; to run a stage; to run a machine; to run a rope through a block.
    • Run To cause to stand as a candidate for office; to support for office; as, to run some one for Congress.
    • Run To conduct; to manage; to carry on; as, to run a factory or a hotel.
    • Run To contend in a race; hence, to enter into a contest; to become a candidate; as, to run for Congress.
    • Run To continue in operation; to be kept in action or motion; as, this engine runs night and day; the mill runs six days in the week.
    • Run To continue without falling due; to hold good; as, a note has thirty days to run .
    • Run To creep, as serpents.
    • Run To discharge pus or other matter; as, an ulcer runs .
    • Run To discharge; to emit; to give forth copiously; to be bathed with; as, the pipe or faucet runs hot water. "At the base of Pompey's statua,
      Which all the while ran blood, great Cæsar fell."
    • Run To discuss; to continue to think or speak about something; -- with on.
    • Run To drive or force; to cause, or permit, to be driven. "They ran the ship aground.""A talkative person runs himself upon great inconveniences by blabbing out his own or other's secrets.""Others, accustomed to retired speculations, run natural philosophy into metaphysical notions."
    • Run To encounter or incur, as a danger or risk; as, to run the risk of losing one's life. See To run the chances, below. "He runneth two dangers.""If we don't succeed, we run the risk of failure."
    • Run To exert continuous activity; to proceed; as, to run through life; to run in a circle.
    • Run To extend; to reach; as, the road runs from Philadelphia to New York; the memory of man runneth not to the contrary.
    • Run To flee, as from fear or danger.
    • Run To flow, as a liquid; to ascend or descend; to course; as, rivers run to the sea; sap runs up in the spring; her blood ran cold.
    • Run To fuse; to shape; to mold; to cast; as, to run bullets, and the like. "The purest gold must be run and washed."
    • Run To go back and forth from place to place; to ply; as, the stage runs between the hotel and the station.
    • Run To go swiftly; to pass at a swift pace; to hasten.
    • Run To go through or accomplish by running; as, to run a race; to run a certain career.
    • Run To have a course or direction; as, a line runs east and west.
    • Run To have a legal course; to be attached; to continue in force, effect, or operation; to follow; to go in company; as, certain covenants run with the land.
    • Run To have growth or development; as, boys and girls run up rapidly.
    • Run To make numerous drafts or demands for payment, as upon a bank; -- with on.
    • Run To make progress; to proceed; to pass.
    • Run To migrate or move in schools; -- said of fish; esp., to ascend a river in order to spawn.
    • Run (Athletics) To move rapidly by springing steps so that there is an instant in each step when neither foot touches the ground; -- so distinguished from walking in athletic competition.
    • Run To move, proceed, advance, pass, go, come, etc., swiftly, smoothly, or with quick action; -- said of things animate or inanimate. Hence, to flow, glide, or roll onward, as a stream, a snake, a wagon, etc.; to move by quicker action than in walking, as a person, a horse, a dog.
    • Run To pass from one state or condition to another; to come into a certain condition; -- often with in or into; as, to run into evil practices; to run in debt.
    • Run To pass or go quickly in thought or conversation; as, to run from one subject to another.
    • Run To proceed along a surface; to extend; to spread.
    • Run To pursue in thought; to carry in contemplation. "To run the world back to its first original.""I would gladly understand the formation of a soul, and run it up to its “punctum saliens.”"
    • Run To put at hazard; to venture; to risk. "He would himself be in the Highlands to receive them, and run his fortune with them."
    • Run To sail before the wind, in distinction from reaching or sailing closehauled; -- said of vessels.
    • Run To sew, as a seam, by passing the needle through material in a continuous line, generally taking a series of stitches on the needle at the same time.
    • Run To spread and blend together; to unite; as, colors run in washing.
    • Run To steal off; to depart secretly.
    • Run (Golf) To strike (the ball) in such a way as to cause it to run along the ground, as when approaching a hole.
    • Run To tease with sarcasms and ridicule.
    • Run To tend, as to an effect or consequence; to incline.
    • Run To travel; to make progress; to be moved by mechanical means; to go; as, the steamboat runs regularly to Albany; the train runs to Chicago.
    • Run To turn, as a wheel; to revolve on an axis or pivot; as, a wheel runs swiftly round.
    • ***
Chambers's Twentieth Century Dictionary
  • Interesting fact: A crocodile can run up to a speed of 11 miles per hour
    • v.i Run run to move swiftly on the legs, to hasten, rush on: to move, travel, ply regularly to: to pass by: to have a certain form:
    • v.t Run to cause to move swiftly, to keep running: to force forward: to push: to cause to pass: to fuse: to discharge, as a sore: to pursue in thought: to incur: to pour forth: to execute: to chase: to break through, as to run the blockade: to pierce: to sew: to fish in: to evade: to manage: to tease:—pr.p. run′ning; pa.t. ran; pa.p. run, as 'run brandy,' that which has been smuggled in
    • n Run act of running: course: flow: discharge from a sore: distance sailed: voyage: continued series: general reception: prevalence: popular clamour: an unusual pressure, as on a bank, for payment: a trip: the run of events: a small stream: the quantity run: the act of migrating: in base-ball, the complete circuit made by the player which enables him to score one: in cricket, a passing from one wicket to another, by which one point is scored: a range of pasturage: a pair of millstones: the aftermost part of a ship's bottom:
    • adj Run fleeing from danger or restraint: done by or in flight
    • prep Run (coll.) approaching or about
    • n Run act of moving swiftly: that which runs or flows, the quantity run: a discharge from a wound: the act of one who risks dangers, as in running a blockade: strength to run: the ranging of any animal
    • v.i Run run (law) to have legal authority: to be current, as money: to average: to reach, have course in any direction: to make a fault, to slip, as thread in knitting: to stand as a candidate: to pass from one state to another: to pass quickly in thought, to dwell repeatedly upon in thought: to continue in operation, be in constant motion, to be carried, to extend: to move swiftly: to pass quickly on the ground: to flee: to go, as ships, &c.: to have course in any direction, to extend, spread: to flow: to dart: to turn: to extend through a period: to pierce: to fuse or melt: to turn or rotate: to be busied: to become: to be in force: to discharge matter, as a sore: to have a general tendency: to pass, fall: to creep: to press with immediate demands for payment, as a bank
    • n Run (mus.) a succession of consecutive notes: a roulade
    • ***

Quotations

  • Proverb
    Proverb
    “Some have been thought brave because they didn't have the courage to run away.”
  • Josh Billings
    Josh%20Billings
    “Never run into debt, not if you can find anything else to run into.”
  • Proverb
    Proverb
    “It is better to run back than run the wrong way.”
  • John Johnson
    John Johnson
    “Every day I run scared. That's the only way I can stay ahead.”
  • English Proverb
    English Proverb
    “A hero is a man who is afraid to run away.”
  • Samuel Butler
    Samuel%20Butler
    “Neither have they hearts to stay, nor wit enough to run away.”

Idioms

Cut and run - If people cut and run, they take what they can get and leave before they lose everything.
***
Do the running - (UK) The person who has to do the running has to make sure that things get done. ('Make the running' is also used.)
***
Dry run - A dry run is a full rehearsal or trial exercise of something to see how it will work before it is launched.
***
Give someone a run for their money - If you can give someone a run for the money, you are as good, or nearly as good, as they are at something.
***
Hit the ground running - If someone hits the ground running, they start a new job or position in a very dynamic manner.
***
If you can't run with the big dogs, you'd better stay on the porch - If you can't keep up with what others are doing, then it is best not to attempt it.
***
In the long run - This means 'over a long period of time', 'in the end' or 'in the final result'.
***
In the running - If you have a reasonable chance, you're in the running.
***
In the short run - This refers to the immediate future.
***
Milk run - A milk run is a short trip, stopping in a number of places.
***
On the run - If someone is on the run, they are avoiding arrest and hiding from the police.
***
Out of the gate running - If someone comes out of the gate running, they start something at a fast pace, without any build-up.
***
Run a mile - If someone "Runs a mile", they do everything they can to avoid a situation. Example: "I was worried that he'd take one look at me and run a mile."
***
Run amok - When things or people are running amok, they are wild and out of control.('Run amuck' is also used.)
***
Run around the bush - (USA) If you run around the bush, it means that you're taking a long time to get to the point.
***

Etymology

Webster's Revised Unabridged Dictionary
OE. rinnen, rennen,imp. ran, p. p. runnen, ronnen,). AS. rinnan, to flow (imp. ran, p. p. gerunnen,), and iernan, irnan, to run (imp. orn, arn, earn, p. p. urnen,); akin to D. runnen, rennen, OS. & OHG. rinnan, G. rinnen, rennen, Icel. renna, rinna, Sw. rinna, ränna, Dan. rinde, rende, Goth. rinnan, and perh. to L. oriri, to rise, Gr. to stir up, rouse, Skr. (cf. Origin), or perh. to L. rivus, brook (cf. Rival). √11. Cf. Ember (a.) Rennet

Usage

In literature:

I tried to run my farm and let them hired run the governmint.
"Slave Narratives: A Folk History of Slavery in the United States from Interviews with Former Slaves, Arkansas Narratives, Part 4" by Work Projects Administration
I want a man who can stick his head down and run.
"At Good Old Siwash" by George Fitch
Now they're two runs ahead of us.
"Frank Merriwell's Son" by Burt L. Standish
As soon as he thought all was safe, Jack got out of the copper, and, seizing the harp, was eagerly running off with it.
"Children's Literature" by Charles Madison Curry
The players on each team run in turn, the captains naming who shall run each time.
"Games for the Playground, Home, School and Gymnasium" by Jessie H. Bancroft
But with a bound Alex shot forward on the run, made the remaining distance, and was out of view.
"The Young Railroaders" by Francis Lovell Coombs
She'll run her plank ashore at three forty-five to the dot!
"The Woman from Outside" by Hulbert Footner
LET RUN, OR LET GO BY THE RUN.
"The Sailor's Word-Book" by William Henry Smyth
On board we have only sufficient for six hours' surface running, while our batteries are not far short of running down.
"The Submarine Hunters" by Percy F. Westerman
It lacked not only top and side-curtains, but even windshield and running-board.
"Free Air" by Sinclair Lewis
I can run that and you can run this, and with care we ought to make some money pretty soon.
"The Wind Before the Dawn" by Dell H. Munger
Yes, we had one woman who was contrary enough to run away: Addie, she run off in the woods.
"Slave Narratives: a Folk History of Slavery in the United States From Interviews with Former Slaves" by Work Projects Administration
Run in, run into the parlour, and see what you'll find there.
"The Wide, Wide World" by Susan Warner
The Sicilian, like his master, Manfred, was clearly a man above the common run.
"The Saracen: Land of the Infidel" by Robert Shea
Now she was able to run full speed away from that house where death and destruction were running riot.
"The Saracen: The Holy War" by Robert Shea
Sometimes he'd be too wild to pitch, he'd break and run and you had to let 'im run himself down.
"Slave Narratives: a Folk History of Slavery in the United States From Interviews with Former Slaves" by Work Projects Administration
The horses were running away!
"The Rushton Boys at Rally Hall" by Spencer Davenport
Oh, sometimes he'd pull up a stick and run a piece with it, but he didn't run very far.
"Slave Narratives: a Folk History of Slavery in the United States From Interviews with Former Slaves." by Work Projects Administration
Scarcely had he done so, when they saw an Indian come running.
"Boys' Book of Frontier Fighters" by Edwin L. Sabin
One of the most attractive avenues in the world runs through the commercial district of the city.
"Seven Legs Across the Seas" by Samuel Murray
***

In poetry:

The frogs sing
Of everything
And children run
As leaves swing.
"Where My Sight Goes" by Yvor Winters
Sure is the summer,
Sure is the sun;
The night and the winter
Away they run.
"Up And-Down" by George MacDonald
And you shall run and wander,
And you shall dream and sing
Of brave things and bright things
Beyond the swallow's wings.
"For a Child" by Fannie Stearns Davis
Thy victories and thy deathless fame
Through the wide world shall run,
And everlasting ages sing
The triumphs thou hast won.
"Hymn 89" by Isaac Watts
As streams take hue from shade and sun,
As runs the life the song must run;
But, glad or sad, to His good end
God grant the varying notes may tend!
"Overruled" by John Greenleaf Whittier
And a kind woman asked them what they wanted.
They said: "To stay all night."
"Run, run away! The faster you run the better!"
She answered in affright.
"Hop-O-My-Thumb" by Clara Doty Bates

In news:

Lee County running back Kenneth Hurley, right, rushed for 242 yards, two touchdowns and now has run for 1,024 yards in just six games this season for the 6-0 Trojans.
Everyone has that magical time when you either settle in for the long run or run for the hills.
On Sunday, Sept 9, 2012, the Massena Firefighters hosted it's second 9/11 Run to Remember 5k run.
In past years, as many as 250 people participated annually in the 5K run, 1 mile fun run and the tot trot.
2012 Kids' Run - 1/4 Mile Run .
Blake Reynolds Memorial Run 10K/5K and 1 Mile Run .
It's a day you can pay tribute to Christopher Matlosz by participating in the "Miles For Matlosz" 5 mile run and 1 mile fun run.
The run takes place Tuesday July 3rd an 6:30 pm (5 mile run starts at 7pm) at Lake Carasaljo in Lakewood.
It's time to lace up your running shoes for the second annual Los Islenos Five Mile Run/Walk.
Here are the A-main runs of some of the worlds top best RC drivers running on IIC's super fast carpet track.
Both Windows RT and Windows 8 will run on nearly identical looking hardware and be able to run applications downloaded from the new Microsoft Store.
Senior running back runs for 263 yards, four TDs.
ESPN's Home Run Tracker analyzes video of each home run hit this season and as far back as 2006.
Baseball games often end with home runs, but until yesterday the team that hit the home run always won.
FBA – Bueltel 5 run (Bueltel run), 8:36.
***

In science:

The idea is to calculate the length of a run of increasing (run-up) or decreasing (run-down) size.
An Introduction to Monte Carlo Simulation of Statistical physics Problem
The idea is to calculate the length of a run of increasing (run-up) or decreasing (run-down) size.
Monte Carlo: Basics
Run Width() returns the number of the running width scheme to be used, 0 means no running.
AMEGIC++ 1.0, A Matrix Element Generator In C++
In the course of a normal event generation run, this communication occurs at two stages: (1) At initilization, to establish the basic parameters of the run as a whole. (2) For each new event that is to be transferred from the MEG to the SHG.
Generic User Process Interface for Event Generators
Rather than run the random walk for exactly n steps, let us run it until it deals with k even bands.
Excited Random Walk
Here the first sum runs over the nodes and the second one runs over the clauses; Z2 (c) is the probability that the clause c would be satisfied in a system where the validity of the clause c is not imposed.
On the probabilistic approach to the random satisfiability problem
The lines in Figure 5 denote the area within which we accepted an ob ject as a GC candidate for our second and third spectroscopic runs (there was no sharpness/FWHM cut for the initial run).
The Globular Cluster System of NGC 5128 I. Survey and Catalogs
In each of our spectroscopic runs, we re-observed ob jects from previous runs to provide a consistent velocity zeropoint.
The Globular Cluster System of NGC 5128 I. Survey and Catalogs
After simplifications we have ˘FA (0) = A − 1, where A runs from one to two as λ runs from infinity to zero.
Dynamics of exponential linear map in functional space
In particular, we study the number of runs and the length of the longest run of “a”, which is typically of order log2 n.
Limit law of the standard right factor of a random Lyndon word
This section deals with the number of runs and the length of the longest run in a random Lyndon word.
Limit law of the standard right factor of a random Lyndon word
Estimate the length Mn of the longest run and the length M a1 n of the largest run of a1 as in lemma 3.5 and lemma 3.6 by using the same estimates on geometrical laws.
Limit law of the standard right factor of a random Lyndon word
One therefore has a running diffusion constant κ(Λ) and a running coupling to the gradient field λ(Λ).
Perturbation theory for the effective diffusion constant in a medium of random scatterer
Let {Xt} and {Yu} be two independent random walks run with deterministic kil ling times TX and TY respectively, run from uniformly chosen starting locations x, y ∈ Gn .
Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs
For a single experiment we here run belief propagation O(105 ) times; running a finite temperature 1RSB scheme that many times would be computationally extremely demanding without further approximations.
Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs
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