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

2022/02/24 by Michaël Ulrich, Ulrich, Michaël
Mathematics · Economics, Econometrics and Finance · #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2202.12344

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→∞, 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.

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