Cutoff profiles for quantum Lévy processes and quantum random transpositions

7 Oct 2020 · Amaury Freslon, Lucas Teyssier, Simeng Wang ·

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.

PDF Abstract

Code

Add Remove Mark official

No code implementations yet. Submit your code now

Edit Social Preview

Cutoff profiles for quantum Lévy processes and quantum random transpositions

Code Edit Add Remove Mark official

Categories

Code

Add Remove Mark official