Relaxation of Product Markov Chains on Product Spaces

The purpose of the paper is studying the relaxation time of product{ type Markov chains on product spaces which approach a product distribution. We determine bounds to approach stationarity for such Markov chains in terms of the mixing times of the component Markov chains. In cases where the component mixing times vary much we propose an optimized visiting scheme which makes such product{type Markov chains comparative to Gibbs{type samplers. We conclude the paper by a discussion of the relaxation of Metropolis{type samplers applied to separable energy functions.