Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Mean square value of exponential sums related to representation of integers as sum of two squares
Mean square limit for lattice points in a sphere
Erratum to the paper "Mean square limit for lattice points in a sphere" (Acta Arith. 68 (1994), 383-393)
Variance of number of lattice points in random narrow elliptic strip
Asymptotics of the partition function of a random matrix model
We prove a number of results concerning the large asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...
Integral representations for multiple Hermite and multiple Laguerre polynomials
We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
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