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Publications [#244284] of Xin Zhou

Papers Published

  1. Deift, P; Kriecherbauer, T; Mclaughlin, KTR; Venakides, S; Zhou, X, Strong asymptotics of orthogonal polynomials with respect to exponential weights, Communications on Pure and Applied Mathematics, vol. 52 no. 12 (January, 1999), pp. 1491-1552 [doi]
    (last updated on 2018/08/16)

    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. © 1999 John Wiley & Sons, Inc.
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