Peter Morfe (Penn State)

Title:Asymptotics of the Resistance of the Critical Series-Parallel Graph via Parabolic PDE Theory

Abstract: I will discuss recent work on the connection between a certain class of recursive distributional equations (RDE's), proposed independently by Gurel-Gurevich and Derrida, and parabolic PDE's.  The class of RDE's in question includes those satisfied by the graph distance and the resistance on the series-parallel graph, a random hierarchical lattice introduced by Hambly and Jordan (2004).  The RDE's are expected to undergo a phase transition.  In the critical setting, I will discuss limit theorems that follow from a PDE-based analysis of CDF's.  In the sub/supercritical setting, there will be a tantalizing connection to the theory of reaction-diffusion equations, particularly the Fisher-KPP equation.