Math @ Duke

Publications [#244284] of Xin Zhou
Papers Published
 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
(1999),
pp. 14911552
(last updated on 2018/05/24)
Abstract: We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = eQ(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 RiemannHilbert problem following [22, 23]. We employ the steepestdescenttype method introduced in [18] and further developed in [17, 19] in order to obtain uniform PlancherelRotachtype 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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