Extension of a theorem of Wschebor to free and matrix Brownian motions
Résumé
In 1992, M. Wschebor proved a theorem on the convergence of small increments of the Brownian motion. Since then, it has been extended to various processes. We prove a version of this theorem for the Hermitian Brownian motion and the free Brownian motion. Since these theorems deal with a convergence to a deterministic limit, we prove also the convergence in distribution of the corresponding fluctuations.
Mots clés
- Random matrices free Brownian motion Wigner chaos limit theorems Hermite polynomials. MSC 2020: 15B52 46L54 60J65 33C45 60F15 60F17
- 60F17
- 60F15
- 33C45
- 60J65
- 46L54
- Hermite polynomials. MSC 2020: 15B52
- limit theorems
- Wigner chaos
- free Brownian motion
- Hermite Polynomials
- Limit Theorems
- Wigner Chaos
- Free Brownian Motion
- Random matrices
Domaines
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