Cutoff profiles for quantum L\'{e}vy processes and quantum random transpositions
Probability
2021-01-05 v2 Operator Algebras
Quantum Algebra
Abstract
We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time . Then, we study the induced classical process on the real line and compute its atoms and density. This enables us to find the cutoff profile, which involves free Poisson distributions and the semi-circle law. We prove similar results for quantum permutations and quantum random transpositions.
Keywords
Cite
@article{arxiv.2010.03273,
title = {Cutoff profiles for quantum L\'{e}vy processes and quantum random transpositions},
author = {Amaury Freslon and Lucas Teyssier and Simeng Wang},
journal= {arXiv preprint arXiv:2010.03273},
year = {2021}
}
Comments
29 pages. The new version contains several improvements of the main results