Random walk on hyperbolic unimodular triangulations and circle packing

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• Dr Gourab Ray, Statistical Laboratory, University of Cambridge
• Tuesday 14 October 2014, 16:30-17:30
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

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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.

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