L\'evy Processes on Quantum Permutation Groups

TL;DR

This paper surveys quantum probability and compact quantum groups, introduces quantum Le9vy processes, and applies the theory to quantum permutation groups, providing explicit examples and classifications.

Contribution

It introduces quantum Le9vy processes on compact quantum groups and applies the theory specifically to quantum permutation groups, including explicit examples and classifications.

Findings

Explicit examples of quantum Le9vy processes on quantum permutation groups

Classification of certain classes of quantum Le9vy processes

Survey of quantum probability and compact quantum groups

Abstract

We describe basic motivations behind quantum or noncommutative probability, introduce quantum L\'evy processes on compact quantum groups, and discuss several aspects of the study of the latter in the example of quantum permutation groups. The first half of this paper is a survey on quantum probability, compact quantum groups, and L\'evy processes on compact quantum groups. In the second half the theory is applied to quantum permutations groups. Explicit examples are constructed and certain classes of such L\'evy processes are classified.