Dull cut off for circulants
Probability
2016-07-21 v2
Abstract
Families of symmetric simple random walks on Cayley graphs of Abelian groups with a bound on the number of generators are shown to never have sharp cut off in the sense of [1], [3], or [5]. Here convergence to the stationary distribution is measured in the total variation norm. This is a situation of bounded degree and no expansion. Sharp cut off or the cut off phenomenon has been shown to occur in families such as random walks on a hypercube [1] in which the degree is unbounded as well as on a random regular graph where the degree is fixed, but there is expansion [4]. Our examples agree with Peres' conjecture in [3] relating sharp cut off, spectral gap, and mixing time.
Cite
@article{arxiv.1208.5235,
title = {Dull cut off for circulants},
author = {Aaron Abrams and Eric Babson and Henry Landau and Zeph Landau and James Pommersheim},
journal= {arXiv preprint arXiv:1208.5235},
year = {2016}
}
Comments
9 pages