Asymptotic analysis of orthogonal polynomials, determinants, and multiple integrals which appear, in particular, in random matrix theory and integrable models.
Spectral properties of quasiperiodic Schroedinger operators.
Measure and Integration, Autumn 2014
Metric spaces and topology, Spring 2014
Selected publications (see also ArXiv.org):
Toeplitz, Hankel determinants, orthogonal polynomials, random matrices, integrable models.
(with P. Deift and A. Its) “Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model. Some history and some recent results”, Commun. Pure Appl. Math. 66 (2013) 1360–1438.
(with P. Deift and A. Its) ''Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities'', Ann. of Math. 174 (2011) 1243--1299
(with T. Claeys and A. Its) ''Emergence of a singularity for Toeplitz determinants and Painleve V'', Duke Math. J. 160 (2011) 207--262
[A review paper] ''Aspects of Toeplitz determinants'', in ''Boundaries and Spectra of Random Walks'' (D. Lenz, F. Sobieczky, W. Woss, editors), Progress in Probability, Birkhaeuser, 2011
(with P. Deift and J. Vasilevska) ''Asymptotics for a determinant with a confluent hypergeometric kernel'', Int. Math. Res. Notices (2010), Article ID rnq150, 44pp.
"Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant", Duke Math. J. 139 (2007) 581--619
(with P. Deift and A. Its) "Asymptotics of the Airy-kernel determinant", Commun. Math. Phys. 278 (2008) 643--678
"Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle", Int. Math. Res. Notices 2004 (2004) 1249--1272
(with S. Jitomirskaya) ''Continuity of the measure of the spectrum for discrete quasiperiodic operators'', Math. Res. Lett. 9 (2002) 413--422
(with E. Korotyaev) ''Spectral estimates for periodic Jacobi matrices'', Commun. Math. Phys. 234 (2003) 512--532
''Bloch electron in a magnetic field and the Ising model'', Phys. Rev. Lett. 85 (2000) 4920--4923
Deift P, Its A, Krasovsky I, 2011, Eigenvalues of Toeplitz matrices in the bulk of the spectrum, Bull. Inst. Math. Acad. Sin. (n. S.) 7 (2012), 437-461
Krasovsky I, 2017, Central Spectral Gaps of the Almost Mathieu Operator, Communications in Mathematical Physics, Vol:351, ISSN:0010-3616, Pages:419-439
et al., 2015, On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential I, Communications in Mathematical Physics, Vol:337, ISSN:0010-3616, Pages:1397-1463
Claeys T, Krasovsky I, 2015, TOEPLITZ DETERMINANTS WITH MERGING SINGULARITIES, Duke Mathematical Journal, Vol:164, ISSN:0012-7094, Pages:2897-2987
Deift P, Its A, Krasovsky I, 2013, Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results, Communications on Pure and Applied Mathematics, Vol:66, ISSN:0010-3640, Pages:1360-1438