An' de dog toated arter dat trange fashun!
"The Death Shot" by Mayne Reid
Seconds, we'll toat our trail-ropes along wi' us.
"The War Trail" by Mayne Reid
Why not toat him along?
"The Free Lances" by Mayne Reid
I must toat him to the shanty; load enough for my old limbs.
"The Fatal Cord" by Mayne Reid
He's boun to be toated.
"The Headless Horseman" by Mayne Reid
The domestics had gone back to the house, "toating" the huge carcass with ropes, and uttering shouts of triumph.
"Osceola the Seminole" by Mayne Reid
She war tryin' to toat you along wi' her.
"The Yellow Chief" by Mayne Reid
Don't ye ever think o' driving that old toat of a tor-toys into my garden, vor if you does I'll kick 'en.
"A Drake by George!" by John Trevena
Dictionaire universel de toates les Sciences, & des Arts 3 Volumes.
"Journal and Letters of Philip Vickers Fithian: A Plantation Tutor of the Old Dominion, 1773-1774." by Philip Vickers Fithian
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In Section 2 we deﬁne the limit on the average, we recall the distinction between thermodynamical transience and recurrence on the average (TOAt and ROAt ) as deﬁned in .
Classification on the average of random walks
Despite its property of symmetry, the simple random walk on a bihomogeneous tree Tn,m (with n 6= m) is neither ROAt nor TOAt (for the proof, see Example 3.11).
Classification on the average of random walks
Whence for any regular λ we obtain Lλ (F (z)) := Lλ (F (·, ·|z)) = 0 which implies that the random walk is λ-TOAt .
Classification on the average of random walks
The previous example, which is locally transient, TOAt and ROA, shows also that while local recurrence imply recurrence on the average, local transience does not imply transience on the average.
Classification on the average of random walks
Also notice that reversed implications are not true, see for instance Example 5.3 (according to this is an example of a mixed TOAt graph).
Classification on the average of random walks
The second one is an example of classiﬁcation on the average with an ICF which appears natural and with respect to which the random walk is ROA and TOAt . 5.3.
Classification on the average of random walks
The simple random walk on X is TOAt with respect to the limit on the average LF .
Classification on the average of random walks
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