72 citations · 191 across the 7 of their papers we have counts for
7 papers
Critical almost Mathieu operator: hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum
Svetlana Jitomirskaya, Simon Becker, Igor Krasovsky
We obtain a representation of the critical almost Mathieu family as a Jacobi matrix that has a singularity. This allows us to prove that the Hausdorff dimension of its spectrum is…
Toeplitz determinants with merging singularities
T. Claeys, I. Krasovsky
We study asymptotic behavior for determinants of Toeplitz matrices corresponding to symbols with two Fisher-Hartwig singularities at the distance from each oth…
On the asymptotics of a Toeplitz determinant with singularities
P. Deift, A. Its, I. Krasovsky
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness…
Toeplitz and Hankel determinants with singularities: announcement of results
P. Deift, A. Its, I. Krasovsky
We obtain asymptotics for Toeplitz, Hankel, and Toeplitz+Hankel determinants whose symbols possess Fisher-Hartwig singularities. Details of the proofs will be presented in another…
Spectral estimates for periodic Jacobi matrices
E. Korotyaev, I. V. Krasovsky
We obtain bounds for the spectrum and for the total width of the spectral gaps for Jacobi matrices on of the form , where $a_…
Bloch electron in a magnetic field and the Ising model
I. V. Krasovsky
The spectral determinant det(H-εI) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux Φ=2πP/Q thr…
Bethe ansatz for the Harper equation: Solution for a small commensurability parameter
I. V. Krasovsky
The Harper equation describes an electron on a 2D lattice in magnetic field and a particle on a 1D lattice in a periodic potential, in general, incommensurate with the lattice pote…