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

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 $U⟨n⟩$ when $m\to \infty$, 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.