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Abstract: Considering quantum random walks, we construct discrete-time approximationsof the eigenvalues processes of minors of Hermitian Brownian motion. It hasbeen recently proved by Adler, Nordenstam and van Moerbeke that the process ofeigenvalues of two consecutive minors of an Hermitian Brownian motion is aMarkov process, whereas if one considers more than two consecutive minors, theMarkov property fails. We show that there are analog results in thenoncommutative counterpart and establish the Markov property of eigenvalues ofsome particular submatrices of Hermitian Brownian motion.



Author: Francois Chapon PMA, Manon Defosseux MAP5

Source: https://arxiv.org/







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