Applications of geometric bounds to the convergence rate of Markov chains on Rn

Quantitative geometric rates of convergence for reversible Markov chains are closely related to the spectral gap of the corresponding operator, which is hard to calculate for general state spaces. This article describes a geometric argumen t to give different types of bounds for spectral gaps of Markov chains on bounded subsets of Rn and to compare the rates of convergence of different Markov chains.