## Talk page

Title:

Newtonian capacity and forests

Speaker:

Abstract:

A uniform spanning forest of Z^d can be thought of as the ‘’uniform measure’’ on forests (collection of trees) of Z^d. The past of a vertex in the uniform spanning forest is the union of the vertex and the finite components that are disconnected from infinity when that vertex is deleted from the forest. In joint work with Hutchcroft we calculate the critical exponent for the intrinsic diameter of the past when d=4. Higher dimensions (mean field case) had been calculated previously by Hutchcroft. An important ingredient of the proof is analysing the Newtonian capacity of the range of a loop erased random walk. In this talk I will also survey recent results obtained in collaboration with Asselah and Schapira on the Newtonian capacity of the range of a simple random walk in Z^4.

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