Conductance and convergence of Markov chains-a combinatorial treatment of expanders

A direct combinatorial argument is given to bound the convergence rate of Markov chains in terms of their conductance (these are statements of the nature 'random walks on expanders converge fast'). In addition to showing that the linear algebra in previous arguments for such results on time-reversible Markov chains was unnecessary, the direct analysis applies to general irreversible Markov chains.>