### On the contact process in an evolving edge random environment

Probability Seminar

11th November 2022, 3:30 pm – 4:30 pm

Fry Building, 2.04

Recently, there has been increasing interest in interacting particle systems on evolving random graphs, respectively in time evolving random environments. In this talk we present some results on the contact process in an evolving edge random environment on (infinite) connected and transitive graphs.

First, we focus on graphs with bounded degree and assume that the evolving random environment is described by an autonomous ergodic spin system with finite range, for example by dynamical percolation. This background process determines which edges are open or closed for infections. Our results concern the dependence of the critical infection rate for survival on the random environment and on the initial configuration of the system. We also consider the phase transition between a trivial/non-trivial upper invariant law and discuss conditions for complete convergence.

Finally, we state some results and open problems in the case of unbounded degree graphs with dynamical percolation as the background such that the contact process evolves on a dynamical long range percolation.

This is joint work with Marco Seiler (University of Frankfurt).

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