The L 2spectral gap of certain positive recurrent Markov chains and jump processes

Abstract

Let D denote the generator of a continuous time positive recurrent Markov process with state space N (or R +). Sufficient conditions are given to imply the existence of β>0 such that if λ≠0 is a point of the spectrum of D considered as an operator on the L 2 space of the equilibrium distribution, then Re(λ)≦−β. A related result is given for discrete time Markov chains.