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The product formula for regularized Fredholm determinants [PDF]
, 2020 For trace class operators A, B B1(H) (H a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the familiar form detH((IH − A)(IH − B)) = detH(IH − A)detH(IH − B).
Gesztesy, Fritz +5 more
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On the numerical evaluation of Fredholm determinants [PDF]
Mathematics of Computation, 2009 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 are of interest, there is no systematic numerical treatment of Fredholm determinants to be ...
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Differential Relations for the Solutions to the NLS Equation and Their Different Representations
Communications in Advanced Mathematical Sciences, 2019 Solutions to the focusing nonlinear Schr\"odinger equation (NLS) of order $N$ depending on $2N-2$ real parameters in terms of wronskians and Fredholm determinants are given.
Pierre Gaillard
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Impurity Green's function of a one-dimensional Fermi gas
Nuclear Physics B, 2015 We consider a one-dimensional gas of spin-1/2 fermions interacting through δ-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function of the ...
Oleksandr Gamayun +2 more
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Intermittency and regularized Fredholm determinants [PDF]
Inventiones Mathematicae, 1999 We consider real-analytic maps of the interval $I=[0,1]$ which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator ${\cal M}$ has a decomposition $Sp ({\cal M}) = σ_c \cup σ_p$ where $σ_c=[0,1]$ is the continuous spectrum of ${\cal M}$ and $σ_p$
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SciPost Physics, 2020 We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk.
Oleksandr Gamayun, Oleg Lychkovskiy, Jean-Sébastien Caux
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From Multiple Integrals to Fredholm Determinants [PDF]
Progress of Theoretical Physics Supplement, 2008 We consider a multiple integral representation for the finite temperature density-density correlation functions of the one-dimensional Bose gas with delta function interaction in the limits of infinite and vanishing repulsion. In the former case a known Fredholm determinant is recovered.
Seel, Alexander +2 more
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Asymptotics of Fredholm Determinant Associated with the Pearcey Kernel [PDF]
Communications in Mathematical Physics, 2021 The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well.
Dan Dai, Shuai-Xia Xu, Lun Zhang
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The Malgrange Form and Fredholm Determinants [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2017 We consider the factorization problem of matrix symbols relative to a closed contour, i.e., a Riemann-Hilbert problem, where the symbol depends analytically on parameters. We show how to define a function $τ$ which is locally analytic on the space of deformations and that is expressed as a Fredholm determinant of an operator of "integrable" type in the
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Fredholm Determinants and the Statistics of Charge Transport [PDF]
Communications in Mathematical Physics, 2008 ISSN:0010 ...
Avron, J. E. +3 more
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