2022-05-29T09:30:27Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000283872021-03-01T10:04:03ZMatrix Liberation Process I: Large Deviation Upper Bound and Almost Sure ConvergenceUeda, Yoshimichi“This is a post-peer-review, pre-copyedit version of an article published in [Journal of Theoretical Probability]. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10959-018-0819-z”.Random matrixStochastic processUnitary Brownian motionLarge deviationLarge N limitFree probabilityWe 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.ファイル公開：2020/06/01Springer2019-06engjournal articlehttp://hdl.handle.net/2237/00030580https://nagoya.repo.nii.ac.jp/records/28387https://doi.org/10.1007/s10959-018-0819-z0894-98401572-9230Journal of Theoretical Probability322806847https://nagoya.repo.nii.ac.jp/record/28387/files/Liberation1-20180215.pdfapplication/pdf249.6 kB2020-06-01