Critical exponents for three-dimensional percolation models with long-range dependence

Abstract: We will report on recent progress regarding the near-critical behavior of certain statistical mechanics models in dimension three. Our results deal with the phase transition associated to two percolation problems involving the Gaussian free field (GFF) in 3D. In one case, they determine a unique “fixed point” corresponding to the transition, which is proved to obey Fisher’s scaling law. This is one of several relations classically conjectured by physicists to hold on the grounds of a corresponding scaling ansatz.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .