Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walk on sparse random digraphs   A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium
remains close to its initial value over a certain number of iterations and then
abruptly drops to near 0 on a much shorter time scale. Originally discovered in
the context of card shuffling (Aldous-Diaconis, 1986), this remarkable
phenomenon is now rigorously established for many reversible chains. Here we
consider the non-reversible case of random walks on sparse directed graphs, for
which even the equilibrium measure is far from being understood. We work under
the configuration model, allowing both the in-degrees and the out-degrees to be
freely specified. We establish the cutoff phenomenon, determine its precise
window and prove that the cutoff profile approaches a universal shape. We also
provide a detailed description of the equilibrium measure.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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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: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: quant-ph