Alexander R. Its
Prof. Its' major area is integrable systems. His current research interests are concentrated in the following directions: (a) Asymptotic analysis of the matrix models and orthogonal polynomials via Riemann-Hilbert and isomonodromy methods; (b) The asymptotic analysis of the correlation functions of quantum exactly solvable models and the related aspects of the theory of Fredholm and Toeplitz operators; (c) The theory of integrable nonlinear partial and ordinary differential equations of the KdV and Painleve types.
A. R. Its, F. Mezzadri, and M. Y. Mo, Entanglement entropy in quantum spin chains with finite range interaction, Communications in Mathematical Physics, vol: 284 (2008), 117-18.
A. Its, I. Krasovsky, Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump, Contemporary Mathematics, v. 458 (2008), 215-247.
A. R. Its, A. B. J. Kuijlaars and J. Ostensson, Critical Edge Behavior in Unitary Random Matrix Ensembles and the Thirty-Fourth Painleve Transcendent, IMRN, Volume 2008: article ID rnn017, (2008) 67 pages.
T. Claeys, A. Its, and I. Krasovsky, Higher order analogues of the Tracy-Widom distribution and the Painleve II hierarchy, to appear in Comm. Pure. Appl. Math. (arxiv:0901.2473)
P. Deift, A. Its, and I. Krasovsky, Asymptotics of Toeplitz, Hankel, and Toeplitz + Hankel determinants with Fisher-Hartwig singularities, preprint, arXiv: 0905.0443
A.R. Its, Asymptotics of Solutions of the Nonlinear Schrodinger Equation and Isomonodromic Deformations of the Systems of Linear Differential Equations, Soviet. Math. Dokl. 24, N 3, p. 452-456 (1981).
A.S. Fokas, A.R. Its and A.V. Kitaev, The Isomonodromy Approach to Matrix Models in 2D Quantum Gravity, Comm. Math. Phys. 147, 395-430 (1992).
P. A. Deift, A. R. Its, X. Zhou, A Riemann-Hilbert Approach to Asymptotic Problems Arising in the Theory of Random Matrix Models, and Also in the Theory of Integrable Statistical Mechanics, Ann. of Math. 146, 149-235 (1997).
P. Bleher, A. Its, Double Scaling Limit in the Random Matrix Model: the Riemann-Hilbert Approach, Communications in Pure and Applied Mathematics, Vol. LVI, (2003) 433 - 516.
P. Deift, A. Its, I. Krasovsky, Asymptotics of the Airy-kernel determinant, Communications in Mathematical Physics 278, 3 643-678 (2008).