# Gibbs states for area-tilted Brownian lines

## Location

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.

The talk will primarily be based on recent joint works with Mriganka Basu Roy Chowdhury (UC Berkeley) and Pietro Caputo (Roma Tre University).