Representation theory and random point processes

TL;DR

This paper explores the connection between noncommutative harmonic analysis on groups and probability theory related to random point processes, providing accessible explanations of key concepts for interdisciplinary understanding.

Contribution

It introduces a novel link between harmonic analysis and random point processes, bridging two previously distant mathematical fields.

Findings

Established a theoretical connection between harmonic analysis and random point processes

Provided accessible explanations of complex mathematical concepts

Extended previous work presented at a major mathematics congress

Abstract

We discuss a connection between two areas of mathematics which until recently seemed to be rather distant from each other: (1) noncommutative harmonic analysis on groups and (2) some topics in probability theory related to random point processes. In order to make the paper accessible to readers not familiar with either of these areas, we explain all needed basic concepts. This is an extended version of G.Olshanski's talk at the 4th European Congress of Mathematics.