Bernoulli Society: One World Probability Webinar #1

Critical long-range percolation

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Abstract
Many statistical mechanics models on the lattice (including percolation, self-avoiding walk, the Ising model and so on) have natural ”long-range” versions in which vertices interact not only with their neighbours, but with all other vertices in a way that decays with the distance. When this decay is described by a power-law, it can lead to new kinds of critical phenomena that are not present in the short-range models. I will describe a new approach to the study of these models that allows us to go well beyond what is known for short-range models, particularly in intermediate dimensions.