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The scaling limit of the 2D discrete Gaussian model at high temperature

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If you have a question about this talk, please contact Perla Sousi .

The discrete Gaussian model is a random lattice field model imitating the Gaussian free field but restricted to taking integer values. Given a lattice, assigning an integer value to each lattice site would give a configuration, and the probability of exhibiting a certain configuration is weighted by measuring the total amount of gradients of the configuration. Because of its relation with some fundamental problems in physics, such as the Kosterlitz-Thouless phase transition in the XY model, this model had drawn the attention of a number of mathematical physicists.

Despite the growing understanding of the topic recently, studying the exact limiting behaviour of related models often turn out to be challenging. In this talk, I will describe why the scaling limit of the 2D discrete Gaussian model can be studied with great precision.

This talk is part of the Probability series.

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