Institute of Mathematics


Modul:   MAT971  Stochastische Prozesse

Scaling limit of the two-dimensional discrete Gaussian model at high temperatures

Talk by Prof. Dr. Pierre-Francois Rodriguez

Date: 18.05.22  Time: 17.15 - 18.15  Room: Y27H12

The discrete Gaussian model is the Gaussian free field conditioned to be integer-valued. As shown rigorously in celebrated work of Fröhlich and Spencer, the conditioning causes a Berezinskii-Kosterlitz-Thouless type phase transition in two dimensions: the interface exhibits a localized low-temperature and a delocalized (rough) high-temperature phase. I will report on recent work with R. Bauerschmidt and J. Park identifying the macroscopic scaling limit of this field in the rough phase, at sufficiently high temperature.