Scaling Limit of the 2d Discrete Gaussian Model

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Abstract:

The Discrete Gaussian model can be seen as the lattice Gaussian free field of variance proportional to a temperature parameter T>0 conditioned to be integer-valued. In two-dimensions, it is a model for a crystal interface undergoing a roughening transition (Kosterlitz--Thousless transition). The existence of this transition was famously proved by Froehlich-Spencer in the 1980s. For high temperatures, we prove that the scaling limit of the Discrete Gaussian model (which is a non-Gaussian field due to the conditioning) is a continuum Gaussian free field at an effective temperature T_eff.

This is joint work with Jiwoon Park and Pierre-Francios Rodriguez.

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai