30 citations · 128 across the 29 of their papers we have counts for
29 papers
Quasi-Pfaffians and applications
Claire Gilson, Shi-Hao Li, Guo-Fu Yu
This paper presents a non-commutative generalization of the Pfaffian which we call a quasi-Pfaffian. This novel concept arises from solving linear systems with non-commutative skew…
Cauchy-Jacobi orthogonal polynomials and the discrete CKP equation
Shi-Hao Li, Satoshi Tsujimoto, Ryoto Watanabe +1
This paper intends to construct discrete spectral transformations for Cauchy-Jacobi orthogonal polynomials, and find its corresponding discrete integrable systems. It turns out tha…
Discrete non-commutative hungry Toda lattice and its application in matrix computation
Zheng Wang, Shi-Hao Li, Kang-Ya Lu +1
In this paper, we plan to show an eigenvalue algorithm for block Hessenberg matrices by using the idea of non-commutative integrable systems and matrix-valued orthogonal polynomial…
Non-intersecting path explanation for block Pfaffians and applications into skew-orthogonal polynomials
Zong-Jun Yao, Shi-Hao Li
In this paper, we mainly consider a combinatoric explanation for block Pfaffians in terms of non-intersecting paths, as a generalization of results obtained by Stembridge. As appli…
On non-commutative leapfrog map
Bao Wang, Shi-Hao Li
We investigate the integrability of the non-commutative leapfrog map in this paper. Firstly, we derive the explicit formula for the non-commutative leapfrog map and corresponding d…
Matrix-valued -deformed bi-orthogonal polynomials, Non-commutative Toda theory and Bäcklund transformation
Claire Gilson, Shi-Hao Li, Ying Shi
This paper is devoted to revealing the relationship between matrix-valued -deformed bi-orthogonal polynomials and non-commutative Toda-type hierarchies. In this procedure, Wrons…
Multiple skew orthogonal polynomials and 2-component Pfaff lattice hierarchy
Shi-Hao Li, Bo-Jian Shen, Jie Xiang +1
In this paper, we introduce multiple skew-orthogonal polynomials and investigate their connections with classical integrable systems. By using Pfaffian techniques, we show that mul…
Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable lattice
Shi-Hao Li, Ying Shi, Guo-Fu Yu +1
Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence…
Discrete orthogonal ensemble on the exponential lattices
Peter J Forrester, Shi-Hao Li, Bo-Jian Shen +1
Inspired by Aomoto's -Selberg integral, the orthogonal ensemble in the exponential lattice is considered in this paper. By introducing a skew symmetric kernel, the configuration…
Dip-ramp-plateau for Dyson Brownian motion from the identity on
Peter J. Forrester, Mario Kieburg, Shi-Hao Li +1
In a recent work the present authors have shown that the eigenvalue probability density function for Dyson Brownian motion from the identity on is an example of a newly iden…
-Pearson pair and moments in -deformed ensembles
Peter J Forrester, Shi-Hao Li, Bo-Jian Shen +1
The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the -lattice setting is considered. We take up the task of initiating a systematic…
Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation
Shi-Hao Li
A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper. The normalization factors of matrix orthogonal polynomials exp…
Moments of quantum purity and biorthogonal polynomial recurrence
Shi-Hao Li, Lu Wei
The Bures-Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statis…
Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials
Bo-Jian Shen, Shi-Hao Li, Guo-Fu Yu
This paper is to evaluate certain Catalan-Hankel Pfaffians by the theory of skew orthogonal polynomials. Due to different kinds of hypergeometric orthogonal polynomials underlying…
Cyclic Pólya Ensembles on the Unitary Matrices and their Spectral Statistics
Mario Kieburg, Shi-Hao Li, Jiyuan Zhang +1
The framework of spherical transforms and Pólya ensembles is of utility in deriving structured analytic results for sums and products of random matrices in a unified way. In the pr…
Asymptotic correlations with corrections for the circular Jacobi -ensemble
Peter J. Forrester, Shi-Hao Li, Allan K. Trinh
Previous works have considered the leading correction term to the scaled limit of various correlation functions and distributions for classical random matrix ensembles and their $β…
Rate of convergence at the hard edge for various Pólya ensembles of positive definite matrices
Peter J. Forrester, Shi-Hao Li
The theory of Pólya ensembles of positive definite random matrices provides structural formulas for the corresponding biorthogonal pair, and correlation kernel, which are well suit…
Christoffel transformations for (partial-)skew-orthogonal polynomials and applications
Shi-Hao Li, Guo-Fu Yu
In this article, we consider the Christoffel transformations for skew-orthogonal polynomials and partial-skew-orthogonal polynomials. We demonstrate that the Christoffel transforma…
Two-parameter generalisations of Cauchy bi-orthogonal polynomials and integrable lattices
Xiang-Ke Chang, Shi-Hao Li, Satoshi Tsujimoto +1
In this article, we consider the generalised two-parameter Cauchy two-matrix model and corresponding integrable lattice equation. It is shown that with parameters chosen as …
Discrete integrable systems and condensation algorithms for Pfaffians
Shi-Hao Li
Inspired by the connection between the Dodgson's condensation algorithm and Hirota's difference equation, we consider condensation algorithms for Pfaffians from the perspectives of…
Classical skew orthogonal polynomials in a two-component log-gas with charges and
Peter J Forrester, Shi-Hao Li
There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue PDF for and invariant random matrix ensembles. Th…
Rank shift conditions and reductions of 2d-Toda theory
Shi-Hao Li, Guo-Fu Yu
This paper focuses on different reductions of 2-dimensional (2d-)Toda hierarchy. Symmetric and skew symmetric moment matrices are firstly considered, resulting in the differential…
Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions
Peter J Forrester, Shi-Hao Li
The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalised to discrete settings involving either a linear or exponential lattic…
Fox H-kernel and -deformation of the Cauchy two-matrix model and Bures ensemble
Peter J Forrester, Shi-Hao Li
A -deformation of the Laguerre weighted Cauchy two-matrix model, and the Bures ensemble, is introduced. Such a deformation is familiar from the Muttalib-Borodin ensemble. The $θ…