Student Probability Seminar

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Percolation and the Discrete Gaussian Free Field

Speaker: Benjamin McKenna, CIMS

Location: Warren Weaver Hall 512

Date: Wednesday, October 3, 2018, noon

Synopsis:

In percolation, one of the main models of statistical mechanics, one considers a family of random subgraphs of a given graph and studies the emergence of an infinite cluster as a model parameter is tuned. This is the famous percolation phase transition. A recent preprint by Duminil-Copin and co-authors establishes this phase transition on a broad class of graphs, via a novel coupling with the discrete Gaussian free field - itself a fundamental random-surface model. This coupling passes through the Ising model, so that the result touches on a greatest-hits album of models in mathematical physics. No prior exposure to any of these three objects will be assumed.