The Analogue of Aldous' spectral gap conjecture for the generalized exclusion process

TL;DR

This paper extends Aldous' spectral gap conjecture to generalized exclusion processes, linking their spectral gaps to those of random walks, thus broadening understanding of spectral properties in stochastic processes.

Contribution

It proves an analogue of Aldous' spectral gap conjecture for generalized exclusion processes, providing an explicit relation to the spectral gap of a random walk.

Findings

Spectral gap of generalized exclusion process is characterized by the spectral gap of a random walk.

The result generalizes previous work on the interchange process.

Provides a new tool for analyzing spectral properties of complex stochastic systems.

Abstract

Caputo, Ligget, and Richthammer proved Aldous' spectral gap conjecture, which asserts that the spectral gaps of a random walk and an interchange process on the common weighted graph are equal. In this paper, we will prove an analogue of Aldous' spectral gap conjecture for generalized exclusion processes, which explicitly describes the spectral gap of a generalized exclusion process by the spectral gap of a random walk.