TPS Seminar today: Monday, April 21, 3:10-4:00pm

[dda...@gmail.com]

Dear all,

We have probability seminar today from Fardin Syed (U. Toronto) in the usual time and place (Fields 210, 3:10-4:00pm).

Best,

Duncan

Title: The KPZ Line Ensemble Converges to Positive Infinity

Abstract: The Airy Line Ensemble is an infinite collection of random, non-intersecting curves obtained by taking an edge scaling limit of Dyson Brownian motion. It plays a key role in the Kardar-Parisi-Zhang (KPZ) Universality Class due to its close connection with the universal random metric known as the Directed Landscape. In this talk, we will discuss a closely related collection of random curves known as the KPZ Line Ensemble, which can loosely be interpreted as a positive temperature analog of the Airy Line Ensemble. The KPZ Line Ensemble possesses properties similar to those of the Airy Line Ensemble, such as stationarity with respect to a parabola and a spatial Markovian Property. Furthermore, it has previously been shown that the KPZ Line Ensemble converges to the Airy Line Ensemble under the KPZ 1:2:3 scaling. For these reasons, one might believe that the bulk of the KPZ Line Ensemble also resembles the Airy Line Ensemble. In this talk, we deduce the asymptotic heights of the lines within the KPZ Line Ensemble and demonstrate that the bulk properties of the two line ensembles differ remarkably. In particular, we will show that while the lines in the Airy Line Ensemble converge to negative infinity in the line index, for the KPZ Line Ensemble they converge to positive infinity.