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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Recurrence of planar graph limits

## Recurrence of planar graph limitsAdd to your list(s) Download to your calendar using vCal - Gurel Gurevich , O (Hebrew University of Jerusalem)
- Wednesday 22 April 2015, 15:30-16:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact webseminars. Random Geometry Co-author: Asaf Nacmias (Tel Aviv University) What does a random planar triangulation on n vertices looks like? More precisely, what does the local neighbourhood of a fixed vertex in such a triangulation looks like? When n goes to infinity, the resulting object is a random rooted graph called the Uniform Infinite Planar Triangulation (UIPT). Angel, Benjamini and Schramm conjectured that the UIPT and similar objects are recurrent, that is, a simple random walk on the UIPT returns to its starting vertex almost surely. In a joint work with Asaf Nachmias, we prove this conjecture. The proof uses the electrical network theory of random walks and the celebrated Koebe-Andreev-Thurston circle packing theorem. We will give an outline of the proof and explain the connection between the circle packing of a graph and the behaviour of a random walk on that graph. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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