Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Strong Asymptotics of Planar Orthogonal Polynomials : Gaussian Weight Perturbed by Finite Number of Point Charges. / Lee, Seung Yeop; Yang, Meng.

In: Communications on Pure and Applied Mathematics, Vol. 76, No. 10, 2023, p. 2888-2956.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Lee, SY & Yang, M 2023, 'Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges', Communications on Pure and Applied Mathematics, vol. 76, no. 10, pp. 2888-2956. https://doi.org/10.1002/cpa.22122

APA

Lee, S. Y., & Yang, M. (2023). Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges. Communications on Pure and Applied Mathematics, 76(10), 2888-2956. https://doi.org/10.1002/cpa.22122

Vancouver

Lee SY, Yang M. Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges. Communications on Pure and Applied Mathematics. 2023;76(10):2888-2956. https://doi.org/10.1002/cpa.22122

Author

Lee, Seung Yeop ; Yang, Meng. / Strong Asymptotics of Planar Orthogonal Polynomials : Gaussian Weight Perturbed by Finite Number of Point Charges. In: Communications on Pure and Applied Mathematics. 2023 ; Vol. 76, No. 10. pp. 2888-2956.

Bibtex

@article{cb8e21a965864bf6ba7892ecf4a298c4,
title = "Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges",
abstract = "We consider the orthogonal polynomial pn(z) with respect to the planar measure supported on the whole complex plane (Formula presented.) where dA is the Lebesgue measure of the plane, N is a positive constant, {c1, …, cν} are nonzero real numbers greater than −1 and (Formula presented.) are distinct points inside the unit disk. In the scaling limit when n/N = 1 and n → ∞ we obtain the strong asymptotics of the polynomial pn(z). We show that the support of the roots converges to what we call the “multiple Szeg{\H o} curve,” a certain connected curve having ν + 1 components in its complement. We apply the nonlinear steepest descent method [9,10] on the matrix Riemann-Hilbert problem of size (ν + 1) × (ν + 1) posed in [22].",
author = "Lee, {Seung Yeop} and Meng Yang",
note = "Publisher Copyright: {\textcopyright} 2023 Wiley Periodicals, LLC.",
year = "2023",
doi = "10.1002/cpa.22122",
language = "English",
volume = "76",
pages = "2888--2956",
journal = "Communications on Pure and Applied Mathematics",
issn = "0010-3640",
publisher = "JohnWiley & Sons, Inc.",
number = "10",

}

RIS

TY - JOUR

T1 - Strong Asymptotics of Planar Orthogonal Polynomials

T2 - Gaussian Weight Perturbed by Finite Number of Point Charges

AU - Lee, Seung Yeop

AU - Yang, Meng

N1 - Publisher Copyright: © 2023 Wiley Periodicals, LLC.

PY - 2023

Y1 - 2023

N2 - We consider the orthogonal polynomial pn(z) with respect to the planar measure supported on the whole complex plane (Formula presented.) where dA is the Lebesgue measure of the plane, N is a positive constant, {c1, …, cν} are nonzero real numbers greater than −1 and (Formula presented.) are distinct points inside the unit disk. In the scaling limit when n/N = 1 and n → ∞ we obtain the strong asymptotics of the polynomial pn(z). We show that the support of the roots converges to what we call the “multiple Szegő curve,” a certain connected curve having ν + 1 components in its complement. We apply the nonlinear steepest descent method [9,10] on the matrix Riemann-Hilbert problem of size (ν + 1) × (ν + 1) posed in [22].

AB - We consider the orthogonal polynomial pn(z) with respect to the planar measure supported on the whole complex plane (Formula presented.) where dA is the Lebesgue measure of the plane, N is a positive constant, {c1, …, cν} are nonzero real numbers greater than −1 and (Formula presented.) are distinct points inside the unit disk. In the scaling limit when n/N = 1 and n → ∞ we obtain the strong asymptotics of the polynomial pn(z). We show that the support of the roots converges to what we call the “multiple Szegő curve,” a certain connected curve having ν + 1 components in its complement. We apply the nonlinear steepest descent method [9,10] on the matrix Riemann-Hilbert problem of size (ν + 1) × (ν + 1) posed in [22].

UR - http://www.scopus.com/inward/record.url?scp=85163839824&partnerID=8YFLogxK

U2 - 10.1002/cpa.22122

DO - 10.1002/cpa.22122

M3 - Journal article

AN - SCOPUS:85163839824

VL - 76

SP - 2888

EP - 2956

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 10

ER -

ID: 359652104