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Cutoff for the random walk on random directed graphs

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Originally discovered in the context of card shuffling (Aldous-Diaconis, 80’s), the cutoff phenomenon has since then been established for many reversible Markov chains arising in a broad variety of contexts. In this talk we consider the non-reversible case of random walks on large directed graphs, for which even the equilibrium measure is far from being understood. For most bounded-degree graphs, we establish the cutoff phenomenon, determine its precise window and prove that the cutoff profile approaches a universal shape. This is joint work with Charles Bordenave and Pietro Caputo.

This talk is part of the Probability series.

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