Title: Gibbs states for area-tilted Brownian lines
Speaker: Shirshendu Ganguly
Speaker Info: UC Berkeley
Brief Description: Gibbs states for area-tilted Brownian lines
Special Note:
Abstract:
Gibbsian line ensembles have been the topic of much recent interest at the interface of probability and statistical physics, most prominently via the Airy line ensemble occurring as a scaling limit of Dyson Brownian motion. Recently, Caputo, Ioffe and Wachtel [CIW] have proposed an area-tilted variant of this ensemble, satisfying a corresponding Gibbs property, aiming to capture the local behavior of level curves in entropically repulsed 3D Ising interfaces, representing a long line of study originating in Bricmont, El Mellouki and Fröhlich (1986). The Gibbs property developed in CIW naturally leads to the central question of classifying all possible infinite-volume states with this local resampling invariance property. The lack of exchangeability, and by consequence, integrability, renders this problem difficult to attack via established techniques. In this talk, I will review some recent progress in our understanding of such area tilted line ensembles, via developing probabilistic and geometric tools.Date: Tuesday, October 31, 2023The talk will primarily be based on recent joint works with Mriganka Basu Roy Chowdhury (UC Berkeley) and Pietro Caputo (Roma Tre University).