Unimodular uniformization and random walks
Seminar | November 14 | 3-4 p.m. | 1011 Evans Hall
James R. Lee, University of Washington
Consider deforming the path metric of a unimodular random graph by a (unimodular) reweighting of its vertices. In many instances, a well-chosen change of metric can be used to study the spectral measure, estimate the heat kernel, and bound the speed of the random walk. Even for extensively studied models like random planar maps (e.g., the uniform infinite planar triangulation) and critical percolation on Z^2, this approach resolves open questions that did not seem amenable to other methods.