Level lines of the massive planar Gaussian free field

08.04.2024 17:00 - 18:00

Leonie Papon (Durham University)

Abstract: The massive planar Gaussian free field (GFF) is a random distribution defined on a subset of the complex plane. As a random distribution, this field a priori does not have well-defined level lines. In this talk, I will give a meaning to this concept by constructing a coupling between a massive GFF and a random collection of loops, called massive CLE_4, in which the loops can naturally be interpreted as the level lines of the field. This coupling is constructed by appropriately reweighting the law of the standard GFF-CLE_4 coupling. I will then relate massive CLE_4 to a massive version of the Brownian loop soup.

M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli, E. Schertzer
TU Wien, Gußhausstraße 25-25a, 2nd floor, EI 2 Pichelmayer HS