Inhomogeneous percolation on ladder graphs

par Réka Szabó

jeudi 28 mai 2020, 13:30 → 14:30 Europe/Paris

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We define an inhomogeneous percolation model on "ladder graphs" obtained as direct products of an arbitrary graph G = (V;E) and the set of integers (vertices are thought of as having a "vertical" component indexed by an integer). We make two natural choices for the set of edges, producing an unoriented graph and an oriented graph. These graphs are endowed with percolation configurations in which independently, edges inside a fixed infinite "column" are open with probability q, and all other edges are open with probability p. For all fixed q one can define the critical percolation threshold p_c(q). We show that this function is continuous in (0, 1). Joint work with Daniel Valesin.

 

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