The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume

A. Sinclair and M. Jerrum (1988) derived a bound on the mixing rate of time-reversible Markov chains in terms of their conductance. The authors generalize this result by not assuming time reversibility and using a weaker notion of conductance. They prove an isoperimetric inequality for subsets of a convex body. These results are combined to simplify an algorithm of M. Dyer et al. (1989) for approximating the volume of a convex body and to improve running-time bounds