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

Summary 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 >0 such that if 0 is a point of the spectrum of D considered as an operator on the L ² space of the equilibrium distribution, then Re()–. A related result is given for discrete time Markov chains.