36 citations · 196 across the 30 of their papers we have counts for
5 papers · 1 filter
Supplementary Material for Random Cayley Graphs Project
Jonathan Hermon, Sam Olesker-Taylor
This document contains supplementary material for the main articles in our Random Cayley Graphs project. We prove refined results about simple random walks on the integers and on t…
No percolation at criticality on certain groups of intermediate growth
Jonathan Hermon, Tom Hutchcroft
We prove that critical percolation has no infinite clusters almost surely on any unimodular quasi-transitive graph satisfying a return probability upper bound of the form $p_n(v,v)…
A spectral characterization for concentration of the cover time
Jonathan Hermon
We prove that for a sequence of finite vertex-transitive graphs of increasing sizes, the cover times are asymptotically concentrated if and only if the product of the spectral-gap…
The exclusion process mixes (almost) faster than independent particles
Jonathan Hermon, Richard Pymar
Oliveira conjectured that the order of the mixing time of the exclusion process with -particles on an arbitrary -vertex graph is at most that of the mixing-time of indepe…
A version of Aldous' spectral-gap conjecture for the zero range process
Jonathan Hermon, Justin Salez
We show that the spectral-gap of a general zero range process can be controlled in terms of the spectral-gap of a single particle. This is in the spirit of Aldous' famous spectral-…