Winter Semester 2023/2024
Winter Semester 2024/2025
- V5F2 Selected Topics in Probability Theory - Discrete Random Matrices
Wednesdays 10:15am - 12pm in seminar room 1.008
Description:
This course is concerned with discrete random matrices and their singularity probability. For large n, what is the probability that a random n x n matrix with independent unbiased {1,-1}-entries (i.e. each entry is 1 with probability 1/2 and -1 with probability 1/2) is singular? This is a classical problem in combinatorial random matrix theory, that has been studied intensively for more than 50 years. This course is covering a range of results on this problem, from early work from the 1960's to a breakthrough of Tikhomirov from 2018. Besides the results themselves, a major aim of the course is to discuss the different tools and techniques that are used in the proofs. As a prerequisite, knowledge of basic probability theory (on the level of an introductory course such as “V2F1 Einführung in die Wahrscheinlichkeitstheorie”) is required.