Lecture notes:
Lectures1-2 , Lectures3-4 , Lecture5, Lectures6-7 , Lectures8-9 , Lectures10-11, Lectures12-13, Lectures14-15, Lecture14(full), Lecture16, Lectures17-18 , Lectures19-20, Lectures21-22, Lectures23-24 .
Exam program
Sources
V5F1 Advanced Topics in Probability Theory
Winter semester 2019(-2020)
Time: Wednesday 12-14 and Friday 14-16 (both in Room 0.006, Endenicher Allee 60 ) . Precise timing: Wed: 12.15-13.00, 13.05--13.50, and Friday: 14.15-15.00, 15.05--15.50. First lecture is on 9 October.
Lecturer: Alexey Bufetov (alexey.bufetov AT gmail.com)
Prerequisites: Basic Probability (e.g., what is a random variable ?). The rest will be defined and explained.
Preliminary plan of the course:
The course is devoted to the study of asymptotic behavior of random surfaces which appear in various problems coming from combinatorics and mathematical physics.
The first part of the course will follow the book ``The surprising mathematics of longest increasing subsequences" by Dan Romik. It can be downloaded on the author's webpage . We will cover Chapter 1 and parts of Chapters 3 and 4.
The second part of the course will be devoted to the study of random tilings of general domains. The main goal is to discuss results from https://arxiv.org/abs/math/0008220
I will also use some material from http://www.math.columbia.edu/~okounkov/AMScolloq.pdf .
The course will have minimal to no overlaps with my last year course