I am pleased to announce the following seminar: Hugo Vanneuville (Université Grenoble Alpes) A new proof of exponential decay in percolation Thursday 22 January at 11:00 Room U9-05 (Building U9, Viale dell'Innovazione 10, Milan) An abstract follows below. All interested participants are welcome. Best regards, Francesco Caravenna %%%%%%%%%%%%%%%%%%%%%%%%%% Abstract. Bernoulli percolation of parameter p on Z^d is defined by keeping each edge of Z^d with probability p, independently of the other edges. The exponential decay theorem - proven in 1987 by Menshikov and independently by Aizenman and Barsky - can be stated as follows: If the cardinality of the cluster of 0 is a.s. finite at some parameter p, then it has an exponential moment at every parameter q<p. I like to state this theorem this way because it illustrates the fact that "decreasing p infinitesimally has a regularising effect on the clusters". The goal of this talk is to discuss this theorem and to propose a new proof. Contrary to the other proofs, we do not rely on differential inequalities but rather on stochastic comparisons. %%%%%%%%%%%%%%%%%%%%%%%%%% -- __________________________________ Francesco Caravenna Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca https://fcaraven.github.io/ __________________________________