Venue: Chern Lecture Hall
Class Timings: Wednesdays from 2:00 PM - 5:00 PM
First Meeting: 7 August 2024
Course Description: This course will consist of two (independent) modules each taught by one of the instructors: one on percolation (Basu) and the other on random matrices (Basak). The duration of each module will be five weeks.
Module I (percolation): This module will be an introduction to the classical theory of Bernoulli percolation on the Euclidean lattice covering the existence of subcritical and supercritical regimes, uniqueness of infinite cluster and sharpness of phase transition, as well as Kesten’s theorem and RSW theory for planar critical percolation. Time permitting, we may also discuss some related models.
Module II (random matrices): This module will introduce techniques to understand spectral statistics of large random self-adjoint matrices, both on global and local scales. The first half will focus on invariant ensembles, while the latter half will be devoted to the universality aspects of such spectral statistics for a wide class of random self-adjoint matrices.
Course Evaluation: Module I Homework – 30%, Module II Homework – 30% and Presentation – 40%. Papers for presentation will be suggested by the instructors.
Perquisites: This is a graduate level topics
course meant for students working on (or intending to work on)
probability theory, and is particularly recommended for graduate students planning to work on
discrete probability or random matrices. Students are expected to be proficient in undergraduate
probability, real analysis and linear algebra and familiar with basic complex analysis. While
graduate level measure theoretic probability is not a prerequisite, it might be useful.
In particular, several facts about product spaces and sequences of independent random
variables will be assumed, so familiarity with these topics will be essential.
- Teacher: Anirban Basak
- Teacher: Riddhipratim Basu