Abstract:

Since the works of Menshikov and Aizenman-Barsky it is known that for every p below the critical value for percolation, the probability that two distant points are connected decays exponentially. The constant in the exponent is called the correlation length. We establish bounds for the correlation length as p increases to the critical value valid in any dimension. Joint work with Hugo Duminil-Copin and Vincent Tassion.