Discrete Riemann mapping and the Poisson boundary

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• Agelos Georgakopoulos (University of Warwick)
• Thursday 17 October 2013, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

Answering a question of Benjamini & Schramm, we show that the Poisson boundary of any planar, uniquely absorbing (e.g. one-ended and transient) graph with bounded degrees can be realised geometrically as a circle, namely as the boundary of a tiling of a cylinder by squares. For this, we introduce a general criterion for identifying the Poisson boundary of a stochastic process that might have further applications.

The talk will be self-contained, assuming no prior knowledge of the mentioned terminology, and will contain many pictures.

This talk is part of the Combinatorics Seminar series.

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