278 citations · 1.7k across the 68 of their papers we have counts for
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On determinants of integrable operators with shifts
A. R. Its, K. K. Kozlowski
Integrable integral operator can be studied by means of a matrix Riemann--Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Rieman…
Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model. Some history and some recent results
P. Deift, A. Its, I. Krasovsky
We review some history and some recent results concerning Toeplitz determinants and their applications. We discuss, in particular, the crucial role of the two-dimensional Ising mod…
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…
Eigenvalues of Toeplitz matrices in the bulk of the spectrum
P. Deift, A. Its, I. Krasovsky
The authors analyze the asymptotics of eigenvalues of Toeplitz matrices with certain continuous and discontinuous symbols. In particular, the authors prove a conjecture of Levitin…
Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
P. Deift, A. Its, I. Krasovsky
We study the asymptotics in n for n-dimensional Toeplitz determinants whose symbols possess Fisher-Hartwig singularities on a smooth background. We prove the general non-degenerate…
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…
Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump
A. Its, I. Krasovsky
We obtain asymptotics in n for the n-dimensional Hankel determinant whose symbol is the Gaussian multiplied by a step-like function. We use Riemann-Hilbert analysis of the related…
Asymptotics of the Airy-kernel determinant
P. Deift, A. Its, I. Krasovsky
The authors use Riemann-Hilbert methods to compute the constant that arises in the asymptotic behavior of the Airy-kernel determinant of random matrix theory.
The Widom-Dyson constant for the gap probability in random matrix theory
P. Deift, A. Its, I. Krasovsky +1
In this paper we consider an asymptotic question in the theory of the Gaussian Unitary Ensemble of random matrices. In the bulk scaling limit, the probability that there are no eig…