Research Interests for Xin Zhou
Research Interests: Partial Differential Equations and Integrable Systems
Professor Zhou studies the 1D, 2D inverse scattering theory, using the method of RiemannHilbert problems. His
current research is concentrated in a nonlinear type of microlocal analysis on RiemannHilbert 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.  Recent Publications
 McLaughlin, KTR; Vartanian, AH; Zhou, X, Asymptotics of recurrence relation coefficients, hankel determinant ratios, and root products associated with laurent polynomials orthogonal with respect to varying exponential weights,
Acta Applicandae Mathematicae, vol. 100 no. 1
(2008),
pp. 39104, ISSN 01678019 [doi] [abs]
 with McLaughlin, KTR; Vartanian, AH; Zhou, X, Asymptotics of laurent polynomials of odd degree orthogonal with respect to varying exponential weights,
Constructive Approximation, vol. 27 no. 2
(2008),
pp. 149202, ISSN 01764276 [doi] [abs]
 Rider, B; Zhou, X, Janossy densities for unitary ensembles at the spectral edge,
International Mathematics Research Notices, vol. 2008 no. 1
(2008), ISSN 10737928 [doi] [abs]
 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. 34
(Accepted, 2008),
pp. 187364, ISSN 13850172 [doi] [abs]
 with McLaughlin, KTR; Vartanian, AH, Asymptotics of Coefficients of Recurrence Relations, Hankel Determinants Ratios, and Root Products Associated with Orthogonal Laurent Polynomials with Respect to Varying Exponential Weights,
journal Acta Applicandae Mathematicae, vol. 100
(2008),
pp. 39104
