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Journal of Theoretical Probability

, Volume 32, Issue 2, pp 806–847 | Cite as

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

  • Yoshimichi UedaEmail author
Article
  • 77 Downloads

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 

Mathematics Subject Classification (2010)

60F10 15B52 46L54 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan

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