Related papers: Riemann-Hilbert approach to a generalized sine ker…
In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $\alpha$). In particular, the so-called hard…
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.
We characterize Fredholm determinants of a class of Hankel composition operators via matrix-valued Riemann-Hilbert problems, for additive and multiplicative compositions. The scalar-valued kernels of the underlying integral operators are…
We obtain asymptotics for the Airy kernel Fredholm determinant on two intervals. We give explicit formulas for all the terms up to and including the oscillations of order $1$, which are expressed in terms of Jacobi $\theta$-functions.
We analyze a numerical method for computing Fredholm determinants of trace class and Hilbert Schmidt integral operators defined in terms of matrix-valued kernels on the entire real line. With this method, the Fredholm determinant is…
We investigate a Riemann-Hilbert problem (RHP), whose solution corresponds to a group of $q$-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the…
In the present paper, we consider the integral operator, which acts in Hilbert space and has sine kernel. This operator generates two operator identities and two corresponding canonical differential systems. We find the asymptotics of the…
The regularized trace of the heat kernel of a one-dimensional Schr\"odinger operator with a singular two-particle contact interaction being of Lieb-Liniger type is considered. We derive a complete small-time asymptotic expansion in…
We work out a generalization of the Szeg\"o limit theorems on the determinant of large matrices. We focus on matrices with nonzero leading principal minors and elements that decay to zero exponentially fast with the distance from the main…
We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the…
We obtain the asymptotic expansion for large integer $n$ of a generalised sine-integral \[\int_0^\infty\left(\frac{\sin\,x}{x}\right)^{n}dx\] by utilising the saddle-point method. This expansion is shown to agree with recent results of J.…
We compute the full off-diagonal asymptotics of the equivariant and partial Bergman kernels associated with a circle action on a prequantized K\"ahler manifold with bounded geometry at infinity, then use these results to compute the…
Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency…
In this paper we determine the asymptotics of the determinants of truncated Wiener-Hopf plus Hankel operators $\det(W_R(a)\pm H_R(a))$ as $R$ tends to infinity for symbols $a(x)=(x^2/(1+x^2))^\beta$ with the parameter $\beta$ being of small…
We consider the dynamical correlation functions of the quantum Nonlinear Schrodinger equation. In a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator-valued…
It is shown how classes of Fredholm Pfaffians can be computed in terms of canonical, auxiliary Riemann-Hilbert problems as soon as the main kernel in the Pfaffian is either of additive Hankel composition or of truncated Wiener-Hopf type.…
We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, we study the asymptotic…
Scaling level-spacing distribution functions in the ``bulk of the spectrum'' in random matrix models of $N\times N$ hermitian matrices and then going to the limit $N\to\infty$, leads to the Fredholm determinant of the sine kernel…
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-linear steepest descent method \textit{\'{a} la} Deift-Zhou.…
The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig…