Collision of random walks

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• Perla Sousi (Cambridge)
• Tuesday 02 February 2010, 16:30-17:30
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

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

Regarding his 1920 paper proving recurrence of random walks in Z², Polya wrote that his motivation was to determine whether 2 independent random walks in Z² meet infinitely often. Of course, in this case, the problem reduces to the recurrence of a single random walk in Z², by taking differences. Perhaps surprisingly, however, there exist graphs G where a single random walk is recurrent, yet G has the finite collision property : two independent random walks in G collide only finitely many times almost surely. Some examples were constructed by Krishnapur and Peres (2004), who asked whether critical Galton-Watson trees conditioned on nonextinction also have this property. In this talk I will answer this question as part of a systematic study of the finite collision property. In particular, for two classes of graphs, wedge combs and spherically symmetric trees, we exhibit a phase transition for the finite collision property when growth parameters are varied. I will state the main theorems and give some ideas of the proofs. This is joint work with Martin Barlow and Yuval Peres.

This talk is part of the Probability series.

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