Sharpness of the phase transition for interlacements percolation

In this talk we will review the problem of sharpness in percolation, tracing its origins back to the seminal works of Menshikov, Grimmett-Marstrand and Aizenman-Barsky, which successfully settled the question in the context of Bernoulli independent percolation. Then we will present some recent advancements on the field, which have opened up the possibility of investigating dependent percolation models. Special emphasis will be given to the Interpolation technique, which has proved itself very effective. In particular, it has been used to establish the sharpness for Interlacements Percolation, a model introduced by Sznitman with notoriously intricate dependencies.

This talk is based on a joint work with Duminil-Copin, Goswami, Rodriguez and Severo