140 citations · 609 across the 35 of their papers we have counts for
8 papers · 1 filter
Weingarten calculus for matrix ensembles associated with compact symmetric spaces
Sho Matsumoto
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
Correlation functions for zeros of a Gaussian power series and Pfaffians
Sho Matsumoto, Tomoyuki Shirai
We show that the zeros of the random power series with i.i.d. real Gaussian coefficients form a Pfaffian point process. We further show that the product moments for absolute values…
General moments of matrix elements from circular orthogonal ensembles
Sho Matsumoto
The aim of this paper is to present a systematic method for computing moments of matrix elements taken from circular orthogonal ensembles (COE). The formula is given as a sum of We…
Moments of a single entry of circular orthogonal ensembles and Weingarten calculus
Sho Matsumoto
Consider a symmetric unitary random matrix from a circular orthogonal ensemble. In this paper, we study moments of a single entry . For a dia…
Moments of traces of circular beta-ensembles
Tiefeng Jiang, Sho Matsumoto
Let be random variables from Dyson's circular -ensemble with probability density function $\operatorname {Const}\cdot\prod_{1\leq j<k\leq n}|e^{iθ_j}-e^{iθ_k}|^…
Averages of ratios of characteristic polynomials in circular beta-ensembles and super-Jack polynomials
Sho Matsumoto
We study the averages of ratios of characteristic polynomials over circular -ensembles, where is a positive real number. Using Jack polynomial theory, we obtain three expres…
Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials
Sho Matsumoto
We express the averages of products of characteristic polynomials for random matrix ensembles associated with compact symmetric spaces in terms of Jack polynomials or Heckman and O…
A Scaling Limit for t-Schur Measures
Sho Matsumoto
We introduce a generalization of the Schur measure. And we give a combinatorial interpretation to this generalized measure and prove that a scaling limit for this measure is given…