Modul: MAT971 Stochastische Prozesse

## Strict monotonicity of percolation thresholds under covering maps

Dr. Sébastien Martineau talk

**Date:** 24.10.18 **Time:** 17.15 - 18.15 **Room:** ETH HG G 43

How does the critical parameter of percolation depend on the graph under consideration? Several theorems and conjectures attempt to shed qualitative light on this question, and I will present a recent result fitting this paradigm. If some transitive graph H is a strict quotient of a transitive graph G, then pc(G)<1 => pc(H)>pc(G). We also obtain the same result for the uniqueness parameter pu instead of pc, under the additional assumption that the quotient map has bounded fibres. This is joint work with Franco Severo.