Critical percolation on the hierarchical lattice

Abstract: We consider long-range percolation on the hierarchical lattice, a highly symmetric ultrametric space that serves as a toy model for the Euclidean lattice Z^d. We will outline how to prove up-to-constants estimates on point-to-point connection probabilities for the model at criticality and outline several open problems regarding further critical exponents for the model.

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 .