Orthogonal polynomials, asymptotics, and Heun equations
The Painlevé equations arise from the study of Hankel determinants generated by moment
matrices, whose weights are expressed as the product of “classical” weights multiplied by …
matrices, whose weights are expressed as the product of “classical” weights multiplied by …
Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues
We discuss the recurrence coefficients of the three-term recurrence relation for the
orthogonal polynomials with a singularly perturbed Gaussian weight w (z)=| z| α exp− z 2 …
orthogonal polynomials with a singularly perturbed Gaussian weight w (z)=| z| α exp− z 2 …
Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble
We discuss the monic polynomials of degree n orthogonal with respect to the perturbed
Gaussian weight w (z, t)=| z| α (z 2+ t) λ e− z 2, z∈ R, t> 0, α>− 1, λ> 0, which arises from a …
Gaussian weight w (z, t)=| z| α (z 2+ t) λ e− z 2, z∈ R, t> 0, α>− 1, λ> 0, which arises from a …
On semiclassical orthogonal polynomials associated with a Freud‐type weixght
The recursion relationship: z P n (z)= P n+ 1 (z)+ β n P n− 1 (z), n= 0, 1, 2… is satisfied by all
monic orthogonal polynomials in regard to an arbitrary Freud‐type weight function. In current …
monic orthogonal polynomials in regard to an arbitrary Freud‐type weight function. In current …
Discrete, Continuous and Asymptotic for a Modified Singularly Gaussian Unitary Ensemble and the Smallest Eigenvalue of Its Large Hankel Matrices
D Wang, M Zhu - Mathematical Physics, Analysis and Geometry, 2024 - Springer
This paper focuses on the characteristics of the Hankel determinant generated by a modified
singularly Gaussian weight. The weight function is defined as: w (z; t)=| z| α e-1 z 2-tz 2-1 z 2 …
singularly Gaussian weight. The weight function is defined as: w (z; t)=| z| α e-1 z 2-tz 2-1 z 2 …
Painlevé IV, σ-form, and the deformed Hermite unitary ensembles
We study the Hankel determinant generated by a deformed Hermite weight with one jump w
(z, t, γ)= e− z 2+ tz| z− t| γ (A+ B θ (z− t)), where A≥ 0, A+ B≥ 0, t∈ R, γ>− 1, and z∈ R. By …
(z, t, γ)= e− z 2+ tz| z− t| γ (A+ B θ (z− t)), where A≥ 0, A+ B≥ 0, t∈ R, γ>− 1, and z∈ R. By …
On semi-classical orthogonal polynomials associated with a modified sextic Freud-type weight
Polynomials that are orthogonal with respect to a perturbation of the Freud weight function
by some parameter, known to be modified Freudian orthogonal polynomials, are …
by some parameter, known to be modified Freudian orthogonal polynomials, are …
Semi-classical Orthogonal Polynomials Associated with a Modified Gaussian Weight
Y Ding, C Min - Results in Mathematics, 2024 - Springer
We are concerned with the monic orthogonal polynomials with respect to the modified
Gaussian weight w (x)= w (x; s):= eN [x 2+ s (x 6-x 2)], x∈ R with parameters N> 0 and s∈[0 …
Gaussian weight w (x)= w (x; s):= eN [x 2+ s (x 6-x 2)], x∈ R with parameters N> 0 and s∈[0 …
Laguerre–Hahn orthogonal polynomials on the real line
MDN Rebocho - Random Matrices: Theory and Applications, 2020 - World Scientific
A survey is given on sequences of orthogonal polynomials related to Stieltjes functions
satisfying a Riccati type differential equation with polynomial coefficients—the so-called …
satisfying a Riccati type differential equation with polynomial coefficients—the so-called …
Orthogonal polynomials, bi-confluent Heun equations and semi-classical weights
In this paper, we focus on four weights ω (z, s)= z λ e− N (z+ s (z 2− z)), where z∈(0,∞), λ>−
1, 0≤ s≤ 1, N> 0; ω (z, t)= z λ e− z 2+ tz, where z∈(0,∞), λ>− 1, t∈ R; ω (z, t 1)= e− z 2 A+ B …
1, 0≤ s≤ 1, N> 0; ω (z, t)= z λ e− z 2+ tz, where z∈(0,∞), λ>− 1, t∈ R; ω (z, t 1)= e− z 2 A+ B …