Cutoff for non-backtracking random walks on sparse random graphs
Abstract
A finite ergodic Markov chain is said to exhibit cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card shuffling (Aldous-Diaconis, 1986), this phenomenon is now believed to be rather typical among fast mixing Markov chains. Yet, establishing it rigorously often requires a challengingly detailed understanding of the underlying chain. Here we consider non-backtracking random walks on random graphs with a given degree sequence. Under a general sparsity condition, we establish the cutoff phenomenon, determine its precise window, and prove that the (suitably rescaled) cutoff profile approaches a remarkably simple, universal shape.
Cite
@article{arxiv.1504.02429,
title = {Cutoff for non-backtracking random walks on sparse random graphs},
author = {Anna Ben-Hamou and Justin Salez},
journal= {arXiv preprint arXiv:1504.02429},
year = {2015}
}