Catherine Greenhill
University of New South Wales
Making Markov chains less lazy
There are only a few methods for analysing the rate of convergence of an
ergodic Markov chain to its stationary distribution. One is the
canonical path method of Jerrum and Sinclair. This method applies to
Markov chains which have no negative eigenvalues. Hence it has become
standard practice for theoreticians to work with lazy Markov chains,
which do absolutely nothing with probability 1/2 at each step. This
must be frustrating for practitioners, who want to use the most
efficient Markov chain possible.
I will discuss how laziness can be avoided by the use of a twenty-year
old lemma of Diaconis and Stroock's, or my recent modification of that
lemma. As an illustration, I will apply the new lemma to Jerrum and
Sinclair's well-known chain for sampling perfect matchings in a
bipartite graph.