Summary
Research areas
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.
Teaching
Measure and Integration, autumn 2011, 2012, 2013, 2014, 2016, 2017, 2018.
Distribution Theory, spring 2012.
Metric Spaces and Topology, spring 2013, 2014, 2015.
Probability, spring 2017.
Random Matrices, spring 2017.
Analysis I, spring 2018, 2019.
Fourier Analysis and Distributions, spring 2021.
Selected publications:
Toeplitz, Hankel determinants, orthogonal polynomials, random matrices, integrable models.
"Sine-kernel determinant on two large intervals'' (with B. Fahs), [http://arxiv.org, \\ arXiv:2003.08136]
"Toeplitz determinants with merging singularities'' (with T. Claeys), Duke Math. J. 164 (2015) 2897--2987
''Asymptotics of Toeplitz, Hankel, and Toeplitz Hankel determinants with Fisher-Hartwig singularities'' (with P. Deift and A. Its), Ann. of Math. 174 (2011) 1243--1299
"Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant", Duke Math. J. 139 (2007) 581--619
"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
Quasiperiodic operators
"Critical almost Mathieu operator: Hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum'' (with S. Jitomirskaya) [http://arxiv.org, arXiv:1909.04429]
"Central spectral gaps of the almost Mathieu operator'', Commun. Math. Phys. 351 (2017), 419--439
''Continuity of the measure of the spectrum for discrete quasiperiodic operators'' (with S. Jitomirskaya), Math. Res. Lett. 9 (2002) 413--422
''Bloch electron in a magnetic field and the Ising model'', Phys. Rev. Lett. 85 (2000) 4920--4923
Publications
Journals
Fahs B, Krasovsky I, 2023, Sine-kernel determinant on two large intervals, Communications on Pure and Applied Mathematics, ISSN:0010-3640
Jitomirskaya S, Konstantinov L, Krasovsky I, 2022, On the spectrum of critical almost Mathieu operators in the rational case, Journal of Spectral Theory, Vol:12, ISSN:1664-039X
Fahs B, Krasovsky I, 2019, Splitting of a gap in the bulk of the spectrum of random matrices, Duke Mathematical Journal, Vol:168, ISSN:0012-7094, Pages:3529-3590
Krasovsky I, Bothner T, Its A, et al., 2018, The sine process under the influence of a varying potential, Journal of Mathematical Physics, ISSN:1089-7658
Krasovsky I, 2017, Central Spectral Gaps of the Almost Mathieu Operator, Communications in Mathematical Physics, Vol:351, ISSN:0010-3616, Pages:419-439