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The fredholm determinant method for the KdV equations

Physica D: Nonlinear Phenomena, 1984
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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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A Fredholm Determinant Formula for Section Determinants of Bounded Operators

Integral Equations and Operator Theory, 2004
The author proves a Fredholm determinant formula for section determinants of bounded operators. To be more precise, let \(A\) be a linear bounded operator action on a Hilbert space \(H\) and let \(U:=e^A\) be the exponential function of \(A\). Splitting \(H=H_1\oplus H_2\), where \(H_1\) is finite-dimensional and \(H_2\) is separable, \(U\) can be ...
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Fredholm determinants and multiple solitons

Journal of Mathematical Physics, 1976
The discrete inverse scattering problem in one dimension is considered. Exact solutions are obtained using elementary algebraic tools. Expressions found involve determinants of infinite-dimensional matrices. A simple, heuristic, limiting process yields the solution for the continuous problem.
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Fermion Process and Fredholm Determinant

2000
We construct a family of probability measures on a configuration space associated with Fredholm determinants for symmetric integral operators. For these probability measures we show basic limit theorems (law of large numbers, central limit theorem and large deviation.) Also we deal with shift dynamical systems naturally corresponding to these ...
Tomoyuki Shirai, Yoichiro Takahashi
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Fredholm determinants and Z n -mKdV/Z n -sinh-Gordon hierarchies

International Journal of Nonlinear Sciences and Numerical Simulation, 2022
Chuanzhong Li
exaly  

Integrating evolution equations using Fredholm determinants

Electronic Research Archive, 2021
Feride Tiğlay
exaly  

Fredholm determinants for the Hulthén-distorted separable potential

Pramana - Journal of Physics, 2021
Bidhan Khirali, Ujjwal Laha
exaly  

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