Cube-root fluctuations and Tracy--Widom tails in critically pre-wetted Ising interfaces

Reza Gheissari (U.C. Berkeley)

19-Jun-2020, 17:00-18:00 (4 years ago)

Abstract: Consider the 2D Ising model at low temperature on an $N\times N$ box with minus boundary conditions on the bottom and plus boundary conditions on the other three sides, in the presence of an external field $\lambda \ge 0$. Velenik (2004) proved that in the \emph{critical pre-wetting} regime of $\lambda_N \sim c/N$, the area confined by the interface is $N^{\frac{4}{3}+o(1)}$. Since then more refined features of such interfaces---which have been conjectured to converge to the Ferrari--Spohn diffusion in critically sized $N^{2/3}\times N^{1/3}$ windows--- have only been proven for approximations given by random walks under area tilts.

I will discuss recent work with Shirshendu Ganguly obtaining a more refined understanding of the local and global geometry of the Ising interface in the critical pre-wetting regime. As part of this, we find that its height fluctuations are truly of order $N^{1/3}$, and when they are rescaled by $N^{-1/3}$ they have $\exp( - \Theta(x^{3/2}))$ right tails reminiscent of the Tracy--Widom distribution.

mathematical physicsprobability

Audience: researchers in the topic


Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .

Organizers: Ivan Z Corwin*, Eyal Lubetzky*
*contact for this listing

Export talk to