Related papers: Numerical Fredholm determinants for matrix-valued …
We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green's functions associated with closed ordinary differential…
Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution functions in random matrix theory. Though their numerical values…
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (phi(x) psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm determinants of…
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…
In this paper, we study an infinite system of Fredholm series of polynomials in $\lambda$, formed, in the classical way, for a continuous Hilbert-Schmidt kernel on $\mathbb{R}\times\mathbb{R}$ of the form…
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…
We study the one parameter family of Fredholm determinants $\det(I-\gamma K_{\textnormal{csin}}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{\textnormal{csin}}$ acting on the interval $(-s,s)$ whose kernel is a cubic…
We study the Fredholm determinant of an integrable operator acting on the interval $(0,s)$ whose kernel is constructed out of a hierarchy of higher order analogues to the Painlev\'{e} III equation. This Fredholm determinant describes the…
We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in various random matrix and statistical physics models. We…
In this paper, we consider the deformed Fredholm determinant of the confluent hypergeometric kernel. This determinant represents the gap probability of the corresponding determinantal point process where each particle is removed…
It was proved by Akemann, Ipsen and Kieburg that squared singular values of products of $M$ complex Ginibre random matrices form a determinantal point process whose correlation kernel is expressible in terms of Meijer's $G$-functions.…
A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis Quadrature for Fredholm integral equations of the second kind, whose kernel is either discontinuous or not smooth along the main diagonal, is…
For any integral operator $K$ in the Schatten--von Neumann classes of compact operators and its approximated operator $K_N\sim(N\ge1)$ obtained by using for example a quadrature or projection method, we show that the convergence of the…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
In the bulk scaling limit of the Gaussian Unitary Ensemble of Hermitian matrices the probability that an interval of length $s$ contains no eigenvalues is the Fredholm determinant of the sine kernel $\sin(x-y)\over\pi(x-y)$ over this…
The principal aim in this paper is to develop an effective and unified approach to the computation of traces of resolvents (and resolvent differences), Fredholm determinants, $\zeta$-functions, and $\zeta$-function regularized determinants…
We introduce an appropriate notion of trace in the setting of quaternionic linear operators, arising from the well-known companion matrices. We then use this notion to define the quaternionic Fredholm determinant of trace-class operators in…
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 the pure sine kernel arising in the theory of random…
The diagonal spin-spin correlations of the square lattice Ising model, originally expressed as Toeplitz determinants, are given by two distinct Fredholm determinants - one with an integral operator having an Appell function kernel and…
The aim of this paper is twofold: On one hand we discuss an abstract approach to symmetrized Fredholm perturbation determinants and an associated trace formula for a pair of operators of positive-type, extending a classical trace formula.…