HASEBE Takahiro
Associate Professor
Probability theory for non-commuting variables
Department of Mathematics, Mathematics
| Theme | Noncommutative probability theory |
| Field | Pprobability theory, funcitonal analysis, combinatorics |
| Keyword | Free 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.
