Geometric Convergence and Central Limit Theorems 
for Multidimensional Hastings and  Metropolis Algorithms

by GO Roberts and RLTweedie

Criteria for geometric convergence of multidimensional
Hastings algorithms are given in terms of the tail
behaviour, and the curvature of the contours of the
target density. Conditions leading to non-geometric
convergence are also given, and the results are then
related to the existence of central limit theorems
for moments of the Markov chain.