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

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.