Invited Lecture: Unimodularity and stochastic processes
Saturday, August 6, 2005 - 11:00am - 12:00pm
Russell Lyons (Indiana University)
Stochastic processes on vertex-transitive graphs, especially Cayley graphs of groups, have been studied for 50 years (not counting the special case of integer lattices, which goes back hundreds of years). The assumption of invariance under graph automorphisms plays a key role, but investigations of the last 15 years have shown that an additional assumption is also extremely useful. This newer assumption is the property of unimodularity, which is equivalent to the Mass-Transport Principle. We shall review some well-known applications and also discuss recent work with David Aldous.