Applications of geometric bounds to the convergence rate of Markov chains on R-n

Quantitative geometric rates of convergence for reversible Markov chains ar e closely related to the spectral gap of the corresponding operator, which is hard to calculate for general state spaces. This article describes a geo metric argument to give different types of bounds for spectral gaps of Mark ov chains on bounded subsets of R " and to compare the rates of convergence of different Markov chains. (C) 2000 Elsevier Science B.V. All rights rese rved.