Results 171 to 180 of about 260,310 (201)

A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux [PDF]

Communications in Mathematical Physics, 2001
We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers.
Jinho Baik, Percy Deift, Eric M Rains
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Asymptotics of a Fredholm Determinant Corresponding to the First Bulk Critical Universality Class in Random Matrix Models

Communications in Mathematical Physics, 2014
We study the determinant det(I − KPII) of an integrable Fredholm operator KPII acting on the interval (−s,s) whose kernel is constructed out of the ﰪ-function associated with the Hastings–McLeod solution of the second Painlevé equation.
Thomas Bothner, Alexander Its
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The Fredholm Determinant

2000
In Section 1 we treat the trace and determinant for Fredholm integral operators. For the case of a continuous kernel, this theory was first introduced by Fredholm in the famous paper [Fr]. Some modifications of the Fredholm determinant for integral operators with discontinuous kernels are proposed in Sections 2 and 3.
Israel Gohberg, Seymour Goldberg, Nahum Krupnik   +2 more
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The Fredholm Determinant for a Dirac Operator

Annals of Physics, 1994
The Fredholm determinant for a Dirac operator appropriate to a particle moving in one spatial dimension is investigated. The operator is written as \(H=p_ x\sigma_ 1+ m\sigma_ 3+ V(x)\), where \(p_ x\), \(m\) and \(V(x)\) are, respectively, the momentum, mass, and potential energy of the particle and the Pauli spin matrices, \(\sigma_ i\), constitute a
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Fredholm determinants andτ-functions

Theoretical and Mathematical Physics, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fredholm determinants and the Camassa‐Holm hierarchy

Communications on Pure and Applied Mathematics, 2003
The paper studies the Camassa-Holm (CH) equation \[ \frac {\partial m}{\partial t}=-(mD+Dm)v, \] in which \( D= \partial /{\partial x}\) and \( m=v-v''\): in extenso, \[ \text{CH}:\;\frac {\partial v}{\partial t}-\frac {\partial ^3v}{\partial t\partial x^2}+3v\frac {\partial v}{\partial x}-2\frac {\partial v}{\partial x}\frac {\partial ^2v}{\partial x ...
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Stieltjes imaging of fredholm determinants

Chemical Physics Letters, 1974
Abstract Approximations to Fredholm determinants calculated from the Ritz principle and square-integrable basis functions are interpreted in the context of Stieltjes integration, and shown to provide convergent estimates of elastic scattering phase shifts.
P.W. Langhoff, W.P. Reinhardt
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Completely Monotonic Fredholm Determinants

2020
A functionf(x) is called completely monotonic if (−1)mf(m)(x) > 0. In random matrix theory when the associated orthogonal polynomials have Freud weights, it is known that the expectation of having m eigenvalues of a random Hermitian matrix in an interval is a multiple of (−1)m times the m-th derivative of a Fredholm determinant at λ = 1.
Mourad E. H. Ismail, Ruiming Zhang
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On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities

Physica D: Nonlinear Phenomena
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 the Fisher ...
Yuqiu Zhao, Shuai-Xia Xu, Shu-Quan Zhao   +2 more
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The Fredholm Random Determinants

1990
Let Ξ n be a square random matrix. We call the random function det(I +t Ξ n , where t is a real or complex variable, the Fredholm random determinant of the matrix Ξ n . Fredholm random determinants carry important information about random matrices. With their help, the limiting distributions for eigenvalues of the random matrices can be found.
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