Matrix Liberation Process I: Large Deviation Upper Bound and Almost Sure Convergence
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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.
KeywordsRandom matrix Stochastic process Unitary Brownian motion Large deviation Large N limit Free probability
Mathematics Subject Classification (2010)60F10 15B52 46L54
We would like to express our sincere gratitude to the referee for his/her very careful reading of this paper and pointing out a mistake in the original proof of exponential tightness.
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