Bounds on the 𝐿² spectrum for Markov chains and Markov processes: a generalization of Cheeger’s inequality
Open Access
- 1 January 1988
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 309 (2) , 557-580
- https://doi.org/10.1090/s0002-9947-1988-0930082-9
Abstract
We prove a general version of Cheeger’s inequality for discrete-time 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 L 2 {L^2} exponential convergence to equilibrium for random walk with inward drift on a class of countable rooted graphs.Keywords
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