The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights
[摘要] We consider orthogonal polynomials {p(n,N)(x)}(n=0)(infinity) on the real line with respect to a weight w(x) = e(-NV(x)) and in particular the asymptotic behaviour of the coefficients a(n,N) and b(n,N) in the three-term recurrence x pi(n,N)(x) = pi(n+1,N)(x) + b(n,N) pi(n,N)(x) + a(n,N) pi(n-1,N)(x). For one-cut regular V we show, using the Deift-Zhou method of steepest descent for Riemann-Hilbert problems, that the diagonal recurrence coefficients a(n,n) and b(n,n) have asymptotic expansions as n -> infinity in powers of 1/n(2) and powers of 1/n, respectively. (C) 2009 Elsevier B.V. All rights reserved.
[发布日期] 2009-12-01 [发布机构]
[效力级别] Proceedings Paper [学科分类]
[关键词] Riemann-Hilbert problems;Recurrence coefficients;Orthogonal polynomials;Steepest descent analysis [时效性]
