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Abstract: Geometric rates of convergence for reversible discrete-time Markov chains are closely related to the spectral gap of the corresponding operator. Quantitative geometric bounds on the spectral gap have been developed using the Cheeger's inequality and some path arguments. We extend the discretetime results to continuous-time reversible Markov processes. The limit path bounds and the limit Cheeger's bounds are introduced. Two quantitative examples of 1-dimensional di usions are studied for the... (Update)
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BibTeX entry: (Update)
@misc{ yuen-generalization,
author = "Wai Kong Yuen",
title = "Generalization of Discrete-time Geometric Bounds to Convergence Rate of
Markov Processes on R^n",
url = "citeseer.ist.psu.edu/article/yuen01generalization.html" }
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