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Random walk on hyperbolic unimodular triangulations and circle packing

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Abstract: We investigate the behaviour of random walk on the circle packing of a hyperbolic unimodular triangulations. A way to relate the geometry of such graphs with random walks is via circle packing: one can draw non-intersecting circles on the plane, one for each vertex and circles touch each other if and only if their vertices are adjacent. We show that such a triangulation can be packed in the unit disc and the unit circle gives a pretty accurate description of the final behaviour of the simple random walk on it. Joint work with Omer Angel, Tom Hutchcroft and Asaf Nachmias.

This talk is part of the Probability series.

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