278 citations · 1.7k across the 68 of their papers we have counts for
28 papers · 1 filter
A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants II
Roozbeh Gharakhloo, Alexander Its
In this article, we continue the development of the Riemann-Hilbert formalism for studying the asymptotics of Toeplitz+Hankel determinants with non-identical symbols, which we init…
Connection formulae for the radial Toda equations I
Martin A. Guest, Alexander R. Its, Maksim Kosmakov +2
This paper is the first in a forthcoming series of works where the authors study the global asymptotic behavior of the radial solutions of the 2D periodic Toda equation of type $A_…
Harold Widom's work in random matrix theory
Ivan Corwin, Percy Deift, Alexander Its
This is a survey of Harold Widom's work in random matrices. We start with his pioneering papers on the sine-kernel determinant, continue with his and Craig Tracy's groundbreaking r…
Asymptotics of bordered Toeplitz determinants and next-to-diagonal Ising correlations
Estelle Basor, Torsten Ehrhardt, Roozbeh Gharakhloo +2
We prove the analogue of the strong Szeg{\H o} limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang a…
Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion
L. Brightmore, G. P. Geher, A. R. Its +4
We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, \texttt{arXiv:1104.10…
A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants
Roozbeh Gharakhloo, Alexander Its
In this paper we will formulate Riemann-Hilbert problems for Toeplitz+Hankel determinants and the associated system of orthogonal polynomials, when the Hankel symbol is…
Riemann-Hilbert approach to a generalised sine kernel
R. Gharakhloo, A. R. Its, K. K. Kozlowski
We derive the large distance asymptotics of the Fredholm determinant of the so-called generalised sine kernel at the critical point. This kernel corresponds to a generalisation of…
A representation of joint moments of CUE characteristic polynomials in terms of Painleve functions
Estelle Basor, Pavel Bleher, Robert Buckingham +4
We establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the sigma-Painleve V equatio…
The sine process under the influence of a varying potential
Thomas Bothner, Percy Deift, Alexander Its +1
We review the authors' recent work \cite{BDIK1,BDIK2,BDIK3} where we obtain the uniform large asymptotics for the Fredholm determinant $D(s,γ):=\det(I-γK_s\upharpoonright_{L^2(…
On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo-Miwa-Ueno differential
Thomas Bothner, Alexander Its, Andrei Prokhorov
Several distribution functions in the classical unitarily invariant matrix ensembles are prime examples of isomonodromic tau functions as introduced by Jimbo, Miwa and Ueno (JMU) i…
On the Tracy-Widom Distribution for
Tamara Grava, Alexander Its, Andrey Kapaev +1
We study the Tracy-Widom distribution function for Dyson's -ensemble with . The starting point of our analysis is the recent work of I. Rumanov where he produces a Lax-pai…
On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II
Thomas Bothner, Percy Deift, Alexander Its +1
In this paper we continue our analysis \cite{BDIK} of the determinant where is the trace class operator acting in with kernel $K_s(λ,μ)=\…
Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge
Alexander Bogatskiy, Tom Claeys, Alexander Its
We compute asymptotics for Hankel determinants and orthogonal polynomials with respect to a discontinuous Gaussian weight, in a critical regime where the discontinuity is close to…
Connection problem for the tau-function of the Sine-Gordon reduction of Painlevé-III equation via the Riemann-Hilbert approach
Alexander Its, Andrei Prokhorov
We evaluate explicitly, in terms of the Cauchy data, the constant pre-factor in the large asymptotics of the Painlevé III tau-function. Our result proves the conjectural formul…
Large-x analysis of an operator valued Riemann-Hilbert problem
A. R. Its, K. K. Kozlowski
The purpose of this paper is to push forward the theory of operator-valued Riemann Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-li…
On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential I
Thomas Bothner, Percy Deift, Alexander Its +1
We study the determinant , of the integrable Fredholm operator acting on the interval with kernel . This…
Connection problem for the sine-Gordon/Painlevé III tau function and irregular conformal blocks
A. Its, O. Lisovyy, Yu. Tykhyy
The short-distance expansion of the tau function of the radial sine-Gordon/Painlevé III equation is given by a convergent series which involves irregular conformal blocks and…
Riemann-Hilbert Approach to the Elastodynamic Equation. Half plane
Alexander Its, Elizabeth Its
We show, how the Riemann-Hilbert approach to the elastodynamic equations, which have been suggested in our preceding papers, works in the half-plane case. We pay a special attentio…
Riemann-Hilbert Approach to the Helmholtz Equation in a quarter-plane. Revisited
Alexander Its, Elizabeth Its
We revisit the Helmholts equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 90s by A. Fokas. We show t…
Asymptotics of a Fredholm determinant involving the second Painlevé transcendent
Thomas Bothner, Alexander Its
We study the determinant of an integrable Fredholm operator acting on the interval whose kernel is constructed out of…
Emergence of a singularity for Toeplitz determinants and Painleve V
T. Claeys, A. Its, I. Krasovsky
We obtain asymptotic expansions for Toeplitz determinants corresponding to a family of symbols depending on a parameter . For positive, the symbols are regular so that the d…
The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain
A. R. Its, V. E. Korepin
Toeplitz matrices have applications to different problems of statistical mechanics. Recently they were used for calculation of entanglement entropy in spin chains. We use the Fishe…
Higher order analogues of the Tracy-Widom distribution and the Painleve II hierarchy
T. Claeys, A. Its, I. Krasovsky
We study Fredholm determinants related to a family of kernels which describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are…
Entanglement entropy in quantum spin chains with finite range interaction
A. R. Its, F. Mezzadri, M. Y. Mo
We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Suc…