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Thick Points of Random Walk and the Gaussian Free Field

Presented by: 
Antoine Jego
Wednesday 18th July 2018 - 09:35 to 09:55
INI Seminar Room 1
We consider the thick points of random walk, i.e. points where the local time is a fraction of the maximum. In two dimensions, we answer a question of Dembo, Peres, Rosen and Zeitouni and compute the number of thick points of planar random walk, assuming that the increments are symmetric and have a finite moment of order two. The proof provides a streamlined argument based on the connection to the Gaussian free field and works in a very general setting including isoradial graphs. In higher dimensions, we show that the number of thick points converges to a nondegenerate random variable and that the maximum of the local times converges to a randomly shifted Gumbel distribution.

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