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Alexander R. Its, Ph.D.

     

Research

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.

Publications & Professional Activities

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).

Honors, Awards and Grants

  • The Prize of the Moscow Mathematical Society (1976)
  • The Prize of the Leningrad Mathematical Society (1981)
  • 2002 Hardy Fellow of the London Mathematical Society
  • 2009 Batsheva de Rothschild Fellow of Israel Academy of Sciences and Humanities
Honorable Lectureships
  • Invited Address to the AMS - MAA - SIAM Joint Mathematical Meetings, January 22, 2000.
  • Hardy lectures to the London (June 21.02) and to the Edinburgh (May 24.02) Mathematical Societies. Series of Hardy lectures in several universities in the UK ( March 12 - June 28, 2002 )
  • Invited Speaker to the IMC 2010