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Quantum Random Walks and Minors of Hermitian Brownian Motion |
Canad. J. Math. 64(2012), 805-821
Published:2011-09-19
Printed: Aug 2012
Printed: Aug 2012
- François Chapon,
- Manon Defosseux,
Abstract
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 a 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.
| Keywords: | quantum random walk, quantum Markov chain, generalized casimir operators, Hermitian Brownian motion, diffusions, random matrices, minor process |
| MSC Classifications: |
46L53 - Noncommutative probability and statistics 60B20 - Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 14L24 - Geometric invariant theory [See also 13A50] |