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.

%%%%%%%%%%%%%%%%%%%%%%%%%%