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Cutoff for random walk on dynamical Erdős–Rényi graph

Published version
Peer-reviewed

Type

Article

Change log

Authors

Sousi, Perla 
Thomas, Sam 

Abstract

We consider dynamical percolation on the complete graph Kn, where each edge refreshes its state at rate μ≪1/n, and is then declared open with probability p=λ/n where λ>1. We study a random walk on this dynamical environment which jumps at rate 1/n along every open edge. We show that the mixing time of the full system exhibits cutoff at logn/μ. We do this by showing that the random walk component mixes faster than the environment process; along the way, we control the time it takes for the walk to become isolated.

Description

Keywords

4901 Applied Mathematics, 49 Mathematical Sciences, 4905 Statistics

Journal Title

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Conference Name

Journal ISSN

0246-0203

Volume Title

56

Publisher

Institute of Mathematical Statistics

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/R022615/1)