Researcher Information

Takahiro Hasebe

Associate Professor

Probability theory for non-commuting variables

Department of Mathematics, Mathematics

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Theme

Noncommutative probability theory

FieldPprobability theory, funcitonal analysis, combinatorics
KeywordFree probability, infinitely divisible distributions, Levy processes, cumulants

Introduction of Research

The meaning of a word changes once the order of the alphabets constituting the word is changed. The theory of non-commutative probability is based on regarding such non-commuting elements as "random variables". How to define "independence" is a central subject to be understood. The applications of this research field include random matrices, quantum information, representation theory of groups and graph theory.

Representative Achievements

T. Hasebe and H. Saigo, The monotone cumulants, Ann. Inst. Henri Poincare Probab. Stat. 47, No. 4 (2011), 1160-1170.
T. Hasebe and S. Thorbjørnsen, Unimodality of the freely selfdecomposable probability laws, J. Theoret. Probab. 29 (2016), Issue 3, 922-940.
O. Arizmendi and T. Hasebe, Limit theorems for free Levy processes, Electron. J. Probab. 23, no. 101 (2018), 36 pp.