Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Date (from‐to) : 2015/04 -2019/03
Author : Sakuma Noriyoshi; Yoshida Hiroaki; Collins Benoit; Hasebe Takahiro; Suzuki Ryoichi; Ueda Yuki
In this research we proved the followings:
(1) We proved that the normal distribution is freely selfdecomposable. It means that free convolution semigroup of normal distributions are unimodal. It has some corollaries. In its proof, we found a necessary and sufficient condition for freely selfdecomposable distributions.
(2) We introduce non-commutative point of view to outlier problem. Based on moment methods, we proved that asymptotic cyclic monotone independence appear in our RMM. For some explicit models, we compute concrete limiting distributions.