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Isomorphism theorems, random walks, and spin systems.

Presented by: 
Tyler Helmuth University of Bristol
Date: 
Monday 3rd December 2018 - 11:00 to 12:30
Venue: 
INI Seminar Room 2
Abstract: 
The celebrated BFS-Dynkin isomorphism theorem relates the local time of a random walk to the square of the Gaussian free field. I will discuss one way to see this connection, and also a similar relation between the local time of the vertex-reinforced jump process and hyperbolic spin models. If time permits I will also discuss an application: proving that the vertex-reinforced jump process is always recurrent in two dimensions.




University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons