Publications [#244288] of Xin Zhou

Papers Published

1. McLaughlin, KTR; Vartanian, AH; Zhou, X, Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I, Mathematical Physics Analysis and Geometry, vol. 11 no. 3-4 (November, 2008), pp. 187-364, Springer Nature, ISSN 1385-0172 [doi]
   (last updated on 2024/04/25)

   Abstract:
   Orthogonal rational functions are characterized in terms of a family of matrix Riemann-Hilbert problems on ℝ, and a related family of energy minimisation problems is presented. Existence, uniqueness, and regularity properties of the equilibrium measures which solve the energy minimisation problems are established. These measures are used to derive a family of 'model' matrix Riemann-Hilbert problems which are amenable to asymptotic analysis via the Deift-Zhou non-linear steepest-descent method. © 2008 Springer Science+Business Media B.V.