Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality

Gregory F. Lawler, Alan D. Sokal
1988 Transactions of the American Mathematical Society  
We prove a general version of Cheeger's inequality for discretetime Markov chains and continuous-time Markovian jump processes, both reversible and nonreversible, with general state space. We also prove a version of Cheeger's inequality for Markov chains and processes with killing. As an application, we prove L2 exponential convergence to equilibrium for random walk with inward drift on a class of countable rooted graphs.
doi:10.2307/2000925 fatcat:bakjwopou5dfxpt6dcbwt5wvwq