论文标题
开放KPZ方程的固定度量的最新进展
Some recent progress on the stationary measure for the open KPZ equation
论文作者
论文摘要
此注释是在Harold Widom的内存中专门的，是我在2021年秋季在MSRI程序中的演讲的扩展版本，“随机矩阵中的普遍性和集成性和交互粒子系统”。我将重点介绍开放KPZ方程的固定度量的行为，这是一种与边界接触的界面增长的范式模型。其中大部分将回顾我与A. Knizel以及H. Shen的联合合作的要素，以及W. Bryc，A。Kuznetsov，Y。Wang和J. Wesolowski，G。Barraquand和P. Le Doussal的随后作品。这一进步的基础是B. derrida，M。Evans，V。Hakim和V. Pasquier的基本工作，从2003年起T. Sasamoto，M。Uchiyama和M. Wadati，以及W. Bryc和J. Wesolowski的基本工作，以及2010年和2017年的W. Bryc和J. Wesolowski。 尽管这项工作并非直接来自Harold Widom自己的作品，但它（以及我的大量研究）受到他和Craig Tracy在ASEP上的工作的启发。
This note, dedicated in Harold Widom's memory, is an expanded version of a lecture I gave in fall 2021 at the MSRI program "Universality and Integrability in Random Matrices and Interacting Particle Systems". I will focus on the behavior of the stationary measure for the open KPZ equation, a paradigmatic model for interface growth in contact with boundaries. Much of this will review elements of my joint work with A. Knizel as well as with H. Shen, as well as subsequent works of W. Bryc, A. Kuznetsov, Y. Wang, and J. Wesolowski and of G. Barraquand and P. Le Doussal. The basis for this advance is fundamental work of B. Derrida, M. Evans, V. Hakim and V. Pasquier from 1993, of T. Sasamoto, M. Uchiyama and M. Wadati from 2003, and of W. Bryc and J. Wesolowski from 2010 and 2017. I will try to explain how all of this fits together, without laboring details for the sake of exposition. Though this work does not directly follow from Harold Widom's own work, it (and a great deal of my research) is very much inspired by his and Craig Tracy's work on ASEP.
