Seminars & Colloquia Calendar

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Special Colloquium

Mixing and hittingĀ times - theory and applications

Jonathan Hermon - Cambridge University

Location:  Hill 705
Date & time: Friday, 30 November 2018 at 2:00PM - 2:50PM

Abstract: We present a collection of results, based on a novel operator maximal inequality approach, providing precise relations between the time it takes a Markov chain to converge to equilibrium and the time required for it to exit from small sets. These refine results of Aldous and Lovasz & Winkler. Among the applications are:

(1) A general characterization of an abrupt convergence to equilibrium phenomenon known as cutoff. Specializing this to Ramanujan graphs and trees.

(2) Proving that the return probability decay is not geometrically robust (resolving a problem of Aldous, Diaconis - Saloff-Coste and Kozma).

(3) Random walk in evolving environment.

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