5 papers
The Berry--Esseen Estimate in the Free Central Limit Theorem
Makoto Maejima, Noriyoshi Sakuma
We consider sums of freely independent self-adjoint random variables that are not necessarily identically distributed. Let denote the distribution of the th summand. We as…
Scaling limit theorem for mixed free and Boolean convolution powers
Hao-Wei Huang, Noriyoshi Sakuma, Pei-Lun Tseng +1
We prove a scaling limit theorem for a double sequence of probability measures involving additive free convolution and additive Boolean convolution . Let be…
Modified ruin probability for a Cramér-Lundberg model driven by a compound mixed Poisson process
Noriyoshi Sakuma, Momoka Tashiro
We study modified ruin probabilities in a Cramér-Lundberg model driven by a compound mixed Poisson process. In the heavy-tailed regime, if the integrated claim-size distribution i…
Generalized Meixner-type free gamma distributions:convolution formulas and potential correspondence
Noriyoshi Sakuma, Yuki Ueda
We introduce and study a class of generalized Meixner-type free gamma distributions ( and ), which includes both the free gamma distributions introd…
Fluctuations of eigenvalues of a polynomial on Haar unitary and finite rank matrices
Benoît Collins, Katsunori Fujie, Takahiro Hasebe +2
This paper calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can…