Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cutoff on trees is rare   We study the simple random walk on trees and give estimates on the mixing and
relaxation time. Relying on a recent characterization by Basu, Hermon and
Peres, we give geometric criteria, which are easy to verify and allow to
determine whether the cutoff phenomenon occurs. We thoroughly discuss families
of trees with cutoff, and show how our criteria can be used to prove the
absence of cutoff for several classes of trees, including spherically symmetric
trees, Galton-Watson trees of a fixed height, and sequences of random trees
converging to the Brownian CRT.

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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org