Matrix Liberation Process I: Large Deviation Upper Bound and Almost Sure Convergence

Yoshimichi Ueda ()
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Yoshimichi Ueda: Nagoya University

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 806-847

Abstract: Abstract We introduce the concept of matrix liberation process, a random matrix counterpart of the liberation process in free probability, and prove a large deviation upper bound for its empirical distribution and several properties on its rate function. As a simple consequence, we obtain the almost sure convergence of the empirical distribution of the matrix liberation process to that of the corresponding liberation process as continuous processes in the large N limit.

Keywords: Random matrix; Stochastic process; Unitary Brownian motion; Large deviation; Large N limit; Free probability; 60F10; 15B52; 46L54 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0819-z

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