  This paper develops the use of Dirichlet forms to deliver proofs of optimal
scaling results for Markov chain Monte Carlo algorithms (specifically,
Metropolis-Hastings random walk samplers) under regularity conditions which are
substantially weaker than those required by the original approach (based on the
use of infinitesimal generators). The Dirichlet form methods have the added
advantage of providing an explicit construction of the underlying
infinite-dimensional context. In particular, this enables us directly to
establish weak convergence to the relevant infinite-dimensional distributions.
