\'Etude spectrale minutieuse de processus moins ind\'ecis que les autres

TL;DR

This paper provides explicit quantitative estimates on the convergence to equilibrium of non-reversible Markov processes, especially in short times, by comparing their L2 distances to those of reversible cases.

Contribution

It introduces explicit formulas for the L2 distance to equilibrium for non-reversible Markov processes and compares these with reversible cases.

Findings

Explicit expressions for L2 distance over time

Comparison between reversible and non-reversible processes

Insights into short-time convergence behavior

Abstract

In this paper we are looking for quantitative estimates for the convergene to equilibrium of non reversible Markov processes, especialy in short times. The models studied are simple enough to get an explicit expression of the L2 distance betweeen the semigroup and the invariant measure throught time and to compare it with the corresponding reversible cases.