TY - JOUR

T1 - Strong asymptotics of orthogonal polynomials with respect to exponential weights

AU - Deift, P.

AU - Kriecherbauer, T.

AU - Mclaughlin, K. T.R.

AU - Venakides, S.

AU - Zhou, X.

PY - 1999/12

Y1 - 1999/12

N2 - We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e-Q(x)dx on the real line, where Q(x) = Σ2mk=0qkxk, q2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem following [22, 23]. We employ the steepest-descent-type method introduced in [18] and further developed in [17, 19] in order to obtain uniform Plancherel-Rotach-type asymptotics in the entire complex plane, as well as asymptotic formulae for the zeros, the leading coefficients, and the recurrence coefficients of the orthogonal polynomials.

AB - We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e-Q(x)dx on the real line, where Q(x) = Σ2mk=0qkxk, q2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem following [22, 23]. We employ the steepest-descent-type method introduced in [18] and further developed in [17, 19] in order to obtain uniform Plancherel-Rotach-type asymptotics in the entire complex plane, as well as asymptotic formulae for the zeros, the leading coefficients, and the recurrence coefficients of the orthogonal polynomials.

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U2 - 10.1002/(sici)1097-0312(199912)52:12<1491::aid-cpa2>3.0.co;2-%23

DO - 10.1002/(sici)1097-0312(199912)52:12<1491::aid-cpa2>3.0.co;2-%23

M3 - Article

AN - SCOPUS:0033459230

VL - 52

SP - 1491

EP - 1552

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 12

ER -