论文信息 - Fredholm determinants and inverse scattering problems

Fredholm determinants and inverse scattering problems

The Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts. The result is an identity relating two different types of Fredholm determinant. As an application of the method, an asymptotic formula of high accuracy is derived for a particular Fredholm determinant that determines the level-spacing distribution-function in the theory of random matrices.

Freeman J. Dyson | F. Dyson

[1] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[2] M. Mehta,et al. Asymptotic behavior of spacing distributions for the eigenvalues of random matrices , 1973 .

[3] Madan Lal Mehta,et al. Random Matrices and the Statistical Theory of Energy Levels. , 1970 .

[4] U. Grenander,et al. Toeplitz Forms And Their Applications , 1958 .

[5] F. Dyson. Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[6] M. Gaudin. Sur la loi limite de l'espacement des valeurs propres d'une matrice ale´atoire , 1961 .

[7] H. Widom. Toeplitz Determinants with Singular Generating Functions , 1973 .

[8] Ronald Arbuthnott Knox,et al. On English translation , 1973 .

[9] H. Widom. The Strong Szego Limit Theorem for Circular Arcs , 1971 .