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Xin Zhou

Professor Emeritus of Mathematics
Mathematics
Box 90320, Durham, NC 27708-0320
PO Box 90320, Durham, NC 27708

Overview


Professor Zhou studies the 1-D, 2-D inverse scattering theory, using the method of Riemann-Hilbert problems. His current research is concentrated in a nonlinear type of microlocal analysis on Riemann-Hilbert problems. Subjects of main interest are integrable and near intergrable PDE, integrable statistical models, orthogonal polynomials and random matrices, monodromy groups and Painleve equations with applications in physics and algebraic geometry. A number of classical and new problems in analysis, numerical analysis, and physics have been solved by zhou or jointly by zhou and his collaborators.

Current Appointments & Affiliations


Professor Emeritus of Mathematics · 2014 - Present Mathematics, Trinity College of Arts & Sciences

Recent Publications


Janossy densities for unitary ensembles at the spectral edge

Journal Article International Mathematics Research Notices · December 1, 2008 For a broad class of unitary ensembles of random matrices, we demonstrate the universal nature of the Janossy densities of eigenvalues near the spectral edge, providing a different formulation of the probability distributions of the limiting second, third, ... Full text Cite

Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I

Journal Article Mathematical Physics Analysis and Geometry · November 1, 2008 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 wh ... Full text Cite

Asymptotics of laurent polynomials of odd degree orthogonal with respect to varying exponential weights

Journal Article Constructive Approximation · March 1, 2008 Let Λ ℝ denote the linear space over ℝ spanned by zk k ℤ. Define the (real) inner product Ċ,Ċ L : Λ ℝ× Λ ℝ ℝ, (f,g) ∫ℝ f(s)g(s) exp(- N V(s)) ds, N ℕ, where V satisfies: (i) V is real analytic on ℝ 0; ... Full text Cite
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Recent Grants


Riemann-Hilbert Problem and Integrable Systems

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2006 - 2010

Riemann-Hilbert problem and integrable systems

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2003 - 2007

Inverse Scattering Theory

ResearchPrincipal Investigator · Awarded by National Science Foundation · 2000 - 2003

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Education, Training & Certifications


University of Rochester · 1988 Ph.D.
Chinese Academy of Sciences (China) · 1982 M.Sc.