Space-time joint laws of the KPZ fixed point

Speaker: 廖羽晨（中国科学技术大学）

Title: Space-time joint laws of the KPZ fixed point

Inviter: 随机分析研究中心

Time & Venue: 2025年7月25日16:00--17:00 南楼613

Abstract: The KPZ fixed point, first constructed by Matetski-Quastel-Remenik, is a universal scaling limit for the so-called Kardar-Parisi-Zhang universality class, a large family of random growth models in 1+1 (space + time) dimension. It can be described as a Markov process on the space of height functions with explicit transition probabilities (fixed time spatial laws). In this talk I will introduce this object and discuss the integrability around it. In particular I will show some new formulas describing the space-time joint laws of this two-dimensional random fields and discuss some applications of the complicated formulas. Based on joint work with Zhipeng Liu.