Vector-valued Gaussian free field conditioned to avoid a ball: Entropic repulsion of the norm and Freezing of spins

by Aleksandra Korzhenkova (EPF Lausanne)

Thursday Jan 29, 2026, 4:30 PM → 6:30 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Motivated by understanding the behavior of spin O(N) models at low temper-
ature, we study the law of the two-dimensional vector-valued Gaussian free
field conditioned to avoid a ball at every site of a subdomain. We prove that,
under this conditioning, the norm of the massless field exhibits entropic repul-
sion, while its angular components (spins) freeze at all mesoscopic scales. A
key step in the analysis is to show that, around any given point in the bulk
of the range, the unconditioned field has no holes. In this talk, I will assume
this result and sketch how it leads to the entropic repulsion and spin-freezing
behavior of the conditioned field. Joint work with A. Sepúlveda

 

https://wt.iam.uni-bonn.de/fileadmin/WT/Inhalt/oberseminar/2026_01_29_Aleksandra_Korzhenkova.pdf