2024-03-29T08:48:14Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00028387
2023-01-16T04:21:02Z
697:698:699
Matrix Liberation Process I: Large Deviation Upper Bound and Almost Sure Convergence
Ueda, Yoshimichi
open access
“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 matrix
Stochastic process
Unitary Brownian motion
Large deviation
Large N limit
Free probability
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.
ファイル公開:2020/06/01
Springer
2019-06
eng
journal article
AM
http://hdl.handle.net/2237/00030580
https://nagoya.repo.nii.ac.jp/records/28387
https://doi.org/10.1007/s10959-018-0819-z
0894-9840
1572-9230
Journal of Theoretical Probability
32
2
806
847
https://nagoya.repo.nii.ac.jp/record/28387/files/Liberation1-20180215.pdf
application/pdf
249.6 kB
2020-06-01