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

With Jiwoon Park (Statslab)

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

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.

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