Winter 2022 STAT 36510

Syllabus for topics course in random growth model and KPZ equation

2022/01/06 update: After some thoughts, I feel it is better to focus on one specific random growth model than including too much materials, we will only talk about the KPZ equation if we have time 🙂

The syllabus is modfied slightly as follows.

Preliminary


Universality in complex random systems is a striking concept which has played a central role in the direction of research within probability, mathematical physics and statistical mechanics. It turns out that a variety of physical systems and mathematical models, including randomly growing interfaces, certain stochastic PDEs, traffic models, all demonstrate the same universal statistical behaviors in their long-time/large-scale limit. These systems are said to lie in the Kardar-Parisi-Zhang (KPZ) universality class. 

In this course, we are going to focus on one fundamental model in this universality class — the corner growth model, which can also viewed as interacting particle system and percolation model.

Here are some contents that we would cover:

The corner growth model and some of its relatives

Deterministic large scale limits

The last-passage Markov chain

Tracy-Widom distribution

Evaluations


The evaluation is based on a written project. The written project provides you with an opportunity to research a topic of personal interest to you (related to the topics of the course). The project should be on the order of 6 pages (hard max of 10 pages) in the standard amsart document class in LaTeX (i.e., no modifications to font or margin size, etc). You will have the opportunity to give a short presentation in the end of the semester.

Lecture note

We will follow the lecture note by Timo Seppalainen: Lecture notes on Corner Growth Model

Handwritten lecture notes:

Lecture 1; Lecture 2; Lecture 3

Office hour

The office hour is flexible and can be scheduled by appointment.

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