Quantum random walks and minors of Hermitian Brownian motion

Details Quantum random walks and minors of Hermitian Brownian motion Quantum random walks and minors of Hermitian Brownian motion

2010-09-04

arxiv.org/abs/1009.0808v1

Mathematics

Probability

Scientific paper

Considering quantum random walks, we construct discrete-time approximations of the eigenvalues processes of minors of Hermitian Brownian motion. It has been recently proved by Adler, Nordenstam and van Moerbeke that the process of eigenvalues of two consecutive minors of an Hermitian Brownian motion is a Markov process, whereas if one considers more than two consecutive minors, the Markov property fails. We show that there are analog results in the noncommutative counterpart and establish the Markov property of eigenvalues of some particular submatrices of Hermitian Brownian motion.

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