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