1 citations · 1 across the 8 of their papers we have counts for
8 papers
An analytic approach to the finite R-transform
Octavio Arizmendi, Katsunori Fujie
We revisit Marcus' finite free analogue of Voiculescu -transform from an analytic viewpoint. By relating the finite free Fourier transform to the Laplace transform, we study the…
Critical points of random polynomials and finite free cumulants
Octavio Arizmendi, Andrew Campbell, Katsunori Fujie
A result of Hoskins and Steinerberger [Int. Math. Res. Not., (13):9784-9809, 2022] states that repeatedly differentiating a random polynomials with independent and identically dist…
Regularity and Convergence Properties of Finite Free Convolutions
Katsunori Fujie
Finite free convolutions, and , are binary operations on polynomials of degree that are central to finite free probability, a developing field at the…
Free probability of type B prime
Katsunori Fujie, Takahiro Hasebe
Free probability of type B was invented by Biane--Goodman--Nica, and then it was generalized by Belinschi--Shlyakhtenko and Février--Nica to infinitesimal free probability. The lat…
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…
New combinatorial identity for the set of partitions and limit theorems in finite free probability theory
Octavio Arizmendi, Katsunori Fujie, Yuki Ueda
We provide a refined combinatorial identity for the set of partitions of , which plays an important role in investigating several limit theorems related to finite f…