中国科大学位与研究生教育
课程名称: 教师:
当前位置:
 >> 
 >> 
An introduction to Kardar–Parisi–Zhang (KPZ) theory
An introduction to Kardar–Parisi–Zhang (KPZ) theory
教师介绍

本讲教师:Zhipeng Liu
所属学科:理科
人  气:405

课程介绍
课程简介:普适性概念与现象,如高斯普适类,广泛出现在复杂结构与随机系统中,在概率,数学物理与统计力学领域中扮演着核心角色。完全不同于涨落指数为1/2的高斯普适类, 涨落指数为1/3的KPZ普适类则刻画了随机增长界面, 一定的随机PDE, 随机矩阵,交互粒子系统与随机环境下聚合物等众多模型的长时间与大尺度统计行为。 本课程内容如下:In the past twenty years, much interest has been focused on a university class, the so-called KPZ universality class, named after Kardar, Parisi and Zhang, who, in 1986, introduced an equation (the KPZ equation) for the growth of random surfaces. It is believed this universality class includes many models in mathematical physics which have the same scaling rates for the time correlations, spatial correlations and the height fluctuations. The limiting fluctuations are also conjectured to be universal and only depend on the initial data. In the talks, we will focus on the most developed model in the KPZ universality class, the totally asymmetric simple exclusion process (TASEP). We will discuss how this model was first solved by using the Robinson-Schensted-Knuth correspondence, a technique in combinatorics, and the orthogonal polynomials. The limiting one point distributions are given by the Tracy-Widom distributions, which were first introduced in the random matrix theory. Then we will consider how to derive the limiting spatial processes, which are called the Airy processes, for some classic initial conditions. In the second part of the talks, we will consider TASEP on a periodic domain. We will show how to obtain the transition probability of periodic TASEP by using the so-called coordinate Bethe ansatz, which was developed in physics and introduced to TASEP by Schutz. Starting from the transition probability formula, we will discuss how to analyze the limiting one point distribution in the so-called relaxation time scale, which is the crossover regime between the Gaussian and KPZ universality. Finally we will discuss some recent results about the limiting space-time fluctuation fields of periodic TASEP in the relaxation time scale.

评论

针对该课程没有任何评论,谈谈您对该课程的看法吧?
  • 用户名: 密 码:
致谢:本课件的制作和发布均为公益目的,免费提供给公众学习和研究。对于本课件制作传播过程中可能涉及的作品或作品部分内容的著作权人以及相关权利人谨致谢意!
课件总访问人次:15383468
中国科学技术大学研究生网络课堂试运行版,版权属于中国科学技术大学研究生院。
本网站所有内容属于中国科学技术大学,未经允许不得下载传播。
地址:安徽省合肥市金寨路96号;邮编:230026。TEL:+86-551-63602922;E-mail:wlkt@ustc.edu.cn。