Probability On Algebraic Structures – POAS

This project will focus on the interaction between probability theory and representation theory, also known as non-commutative harmonic analysis.

Representation theory is the key to solving many models in probability and mathematical physics. In particular, we aim at applying this understanding to integrable models in random matrix theory, last passage percolation and directed polymer models.

Reciprocally, building commutative and non-commutative random walks on algebraic structures sheds new light on their representation theory and deformations (e.g. quantization).
The contributions on this front are a full implementation of Kirillov's orbit method in the context of quantum random walk, and Pitman-type theorems.