My research interests include not only Free Probability Theory itself, but also its applications.
Random Matrix Theory, Statistical Learning Theory, Operator Algebras, Functional analysis, Quantum Information Theory are also in my interests.
T. Hayase, "Free deterministic equivalent Z-scores of compound Wishart models: A goodness of fit test of 2DARMA models",
arXiv preprint arXiv:1710:09497, submitted to a journal.
T. Hayase, "De Finetti theorem for a Boolean anaolgue of easy quantum groups", J. Math. Sci., vol. 24, no. 03, pp. 355~398, 2017 ( arXiv:1507.05563).
The symbol * indicates an invited talk at an international conference.
Cauchy noise loss: A machine learning approach to random matrices and free probability, Noncommutative probability theory and its applications, Ochanomizu University (Japan), Dec., 2017
*De Finetti theorems for a Boolean analogue of easy quantum groups
Free Probability and the Large N Limit, V, UC Berkeley (USA), Mar., 2016
Free product of von Neumann algebras
Workshop of Free monotone transport, Tiba (Japan), Mar., 2016.
Cumulants in noncommutative probability
The 50-th Functional Analysis Workshop, Karuizawa (Japan), Sep., 2015.
A symmetry in free probability: Quantum de Finetti theorem
The 49-th Functional Analysis Workshop, Gifu (Japan), Aug., 2014.
On Cauchy noise loss in a stochastic parameter optimization of random matrices,
Functional analysis seminar, The University of Tokyo (Japan), Feb., 2018
An inverse problem in random matrix theory and free probability theory,
Functional analysis seminar,
Saarland university (Germany), Nov., 2017