Probability seminar: Percolation and isoperimetric inequalities

15 April 2016, 3.40 PM - 15 April 2016, 4.40 PM

Elisabetta Candellero, University of Warwick

SM3, School of Mathematics

Elisabetta Candellero, University of Warwick

Percolation and isoperimetric inequalities

In this talk we will discuss some relations between percolation on a given graph G and its geometry. There are several interesting questions relating various properties of G such as growth (or dimension) and the process of percolation on it. In particular we will look for conditions under which its critical percolation threshold is non-trivial, that is: pc(G) is strictly between zero and one. In a very influential paper on this subject, Benjamini and Schramm asked whether it was true that for every graph satisfying dim(G) > 1, one has pc(G) < 1. We will explain this question in detail and present some recent results that have been obtained in this direction. This talk is based on a joint work with Augusto Teixeira (IMPA, Rio de Janeiro, Brazil).

Contact information

Organisers: Marton Balazs, Haeran Cho

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