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Cutoff profiles for quantum L\'{e}vy processes and quantum random transpositions by Freslon, Amaury; Teyssier, Lucas; Wang, Simeng is a scholarly article available to read on EtoBox.

What is Cutoff profiles for quantum L\'{e}vy processes and quantum random transpositions about?

We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time $N\ln(N)$. 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.

Author

Freslon, Amaury; Teyssier, Lucas; Wang, Simeng

Published

2020

Language

EN