Results 11 to 20 of about 260,310 (201)
On tau functions associated with linear systems [PDF]
, 2012 \noindent {\bf Abstract} This paper considers the Fredholm determinant $\det (I-\Gamma_x)$ of a Hankel integral operator on $L^2(0, \infty )$ with kernel $\phi (s+t+2x)$, where $\phi$ is a matrix scattering function.
Samantha L. Newsham +3 more
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On linear systems and τ functions associated with Lamé's equation and Painlevé's equation VI. [PDF]
, 2011 Painleve's transcendental differential equation PVI may be expressed as the consistency condition for a pair of linear differential equations with 2 by 2 matrix coefficients with rational entries.
Blower, Gordon
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Eigenvalue problem for differential Cauchy-Riemann operator with nonlocal boundary conditions
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 We consider the reduced spectral problem for the Cauchy-Riemann operator with nonlocal boundary conditions to Fredholm linear integral equation of the second kind with a continuous kernel. The corresponding Fredholm determinant is defined for all spectral
Nurlan N Imanbaev
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Unbounded B-Fredholm operators on Hilbert spaces [PDF]
, 2008 This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space H and called B-Fredholm operators.
Berkani, M. +3 more
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Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices
Bulletin of Mathematical Sciences, 2018 We consider a class of Schrödinger operators with complex decaying potentials on the lattice. Using some classical results from complex analysis we obtain some trace formulae and use them to estimate zeros of the Fredholm determinant in terms of the ...
Evgeny Korotyaev, Ari Laptev
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Large fluctuations of the KPZ equation in a half-space
SciPost Physics, 2018 We investigate the short-time regime of the KPZ equation in $1+1$ dimensions and develop a unifying method to obtain the height distribution in this regime, valid whenever an exact solution exists in the form of a Fredholm Pfaffian or determinant ...
Alexandre Krajenbrink, Pierre Le Doussal
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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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Functional equations and separation of variables for exact g-function
Journal of High Energy Physics, 2020 The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate numerically ...
João Caetano, Shota Komatsu
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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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Crossing bridges with strong Szegő limit theorem
Journal of High Energy Physics, 2021 We develop a new technique for computing a class of four-point correlation functions of heavy half-BPS operators in planar N $$ \mathcal{N} $$ = 4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge ...
A. V. Belitsky, G. P. Korchemsky
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