Topic
The Periodic KPZ Fixed Point
Date & Time
Thursday, April 02, 2026 - 17:00 - 18:00
Speaker
Yuchen Liao, University of Science and Technology of China
Location
W923, West Hall, NYU Shanghai New Bund Campus
Abstract:
The KPZ fixed point, first constructed by Matetski, Quastel and Remenik, is a universal scaling limit for a large family of random growth models, known as the Kardar-Parisi-Zhang (KPZ) universality class, in 1+1 dimension. In this talk, I will discuss the analogue of this object on periodic domains, which we call the periodic KPZ fixed point. We derive explicit formulas for the space-time joint distributions of this two-dimensional random field, starting from an arbitrary upper semi-continuous initial condition. It is expected to interpolate the (infinite) KPZ fixed point and the Brownian motion. The formula is obtained by taking scaling limits of formulas of the totally asymmetric simple exclusion process on a ring, under the relaxation time scale t = O(L^{3/2}) where L is the size of the ring.
Based on joint work with Jinho Baik and Zhipeng Liu https://arxiv.org/abs/2603.01964
Biography:
Yuchen Liao is a tenure-track professor from the School of Mathematical Sciences at the University of Science and Technology of China. Prior to joining USTC, he was a Van Vleck visiting assistant professor at the University of Wisconsin-Madison. Before that he was a postdoc research associate at the University of Warwick. He obtained PhD from the University of Michigan supervised by Prof Jinho Baik in 2021. His primary research interests are in probability theory and mathematical physics, in particular integrable probability and KPZ universality.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.