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Isomorphism theorems, random walks, and spin systems.

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SRQ - Scaling limits, rough paths, quantum field theory

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.




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