Thick Points of Random Walk and the Gaussian Free Field

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• Antoine Jego (Cambridge Centre for Analysis)
• Wednesday 18 July 2018, 09:35-09:55
• Seminar Room 1, Newton Institute.

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RGMW06 - RGM follow up

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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