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

Michaël Ulrich

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arXiv · 2202.12344

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

Michaël Ulrich

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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 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.

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Michaël Ulrich. 2022-02-24. On some high-dimensional limits of matricial stochastic processes seen from a quantum probability perspective. https://arxiv.org/abs/2202.12344

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