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arXiv:2202.12344

On some high-dimensional limits of matricial stochastic processes seen from a quantum probability perspective

Ulrich, Michaël

Published Feb 24, 2022• 0 citations
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Abstract

We generalize the result of block-wise convergence of the Brownian motion on the unitary group $U(nm)$ towards a quantum Lévy 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 Lévy process.

DOI
10.48550/arxiv.2202.12344

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