On some high-dimensional limits of matricial stochastic processes seen from a quantum probability perspective
- Resource Type
- Working Paper
- Authors
- Ulrich, Michaël
- Source
- Subject
- Mathematics - Probability
Mathematics - Functional Analysis
46L53 (Primary), 46L54, 60G51, 60B20, 60B15 (Secondary)
- Language
We generalize the result of block-wise convergence of the Brownian motion on the unitary group $U(nm)$ towards a quantum L\'evy process on the unitary dual group $U\langle n\rangle$ when $m\rightarrow\infty$, obtained by the author in a previous paper, by showing that the Brownian motions on the orthogonal group $O(nm)$ and the symplectic group $Sp(nm)$ also converge block-wise to this same quantum L\'evy process.