Syllabus for topic course in random growth model
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
Distributional limit for the last-passage time
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 5 – 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 (20 minutes) in the end of the semester.
We will follow the lecture note by Timo Seppalainen: Lecture notes on Corner Growth Model
Handwritten lecture notes:
The office hour is flexible and can be scheduled by appointment.