Matrix liberation process I: Large deviation upper bound and almost sure convergence
arXiv:1610.04101 · doi:10.1007/s10959-018-0819-z
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 with 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 large limit.
31 pages; to appear J. Theor. Probab