Open Access
August 2019 A version of Aldous’ spectral-gap conjecture for the zero range process
Jonathan Hermon, Justin Salez
Ann. Appl. Probab. 29(4): 2217-2229 (August 2019). DOI: 10.1214/18-AAP1449


We show that the spectral gap of a general zero range process can be controlled in terms of the spectral gap for a single particle. This is in the spirit of Aldous’ famous spectral-gap conjecture for the interchange process, now resolved by Caputo et al. Our main inequality decouples the role of the geometry (defined by the jump matrix) from that of the kinetics (specified by the exit rates). Among other consequences, the various spectral gap estimates that were so far only available on the complete graph or the $d$-dimensional torus now extend effortlessly to arbitrary geometries. As an illustration, we determine the exact order of magnitude of the spectral gap of the rate-one zero-range process on any regular graph and, more generally, for any doubly stochastic jump matrix.


Download Citation

Jonathan Hermon. Justin Salez. "A version of Aldous’ spectral-gap conjecture for the zero range process." Ann. Appl. Probab. 29 (4) 2217 - 2229, August 2019.


Received: 1 October 2018; Published: August 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07120707
MathSciNet: MR3984254
Digital Object Identifier: 10.1214/18-AAP1449

Primary: 60K35

Keywords: Comparison , Dirichlet form , Expanders , mixing time , Particle system , spectral gap , Zero range process

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.29 • No. 4 • August 2019
Back to Top