Probability theory for non-commuting variables
Department of Mathematics, Mathematics
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.