Abstract: The planar vector-valued Gaussian Free Field (GFF) is a Gaussian random field h from Z^2 to R^n which arises naturally in the low-temperature analysis of planar spin-O(N) models \sigma : Z^2 to S^n (with n=N+1).
The purpose of this talk is twofold:
- I will start by describing the geometry of the "level sets" of the vector valued GFF h : Z^2 -> R^n when n \geq 2.
- In the second part, I will explain how the behaviour of these level sets sheds some new light on the conjectural absence of phase transition for 2d spin-O(N) models when N\geq 3 (Polyakov's conjecture, 1975). Our description of the exit sets of the vector valued GFF allows us in particular to revisit a series of works by Patrascioiu-Seiler which questioned Polyakov's prediction.
This is a joint work with Juhan Aru (EPFL) and Avelio Sepúlveda (Universidad de Chili).
Exit sets for vector valued GFF and interplay with planar O(N) models
23.11.2022 16:45 - 17:45
Organiser:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli, E. Schertzer
Location:
HS 21, HP, Stiege 8, Hauptgebäude, Universitätsring 1