Abstract
In this expository article we discuss some questions from the theory of random matrices which have been answered with the help of Toeplitz matrices. These questions concern the statistics of the spacings between eigenvalues of very large hermitian matrices. In certain models of random matrices they lead to the study of the Fredholm determinant of the “sine kernel” sin(x − y)/π(x − y) on a finite interval. This kernel, when discretized, becomes the Toeplitz matrix associated with an arc of the circle and Toeplitz methods help to give the desired answers. Much of this is heuristic, and rigorous proofs are yet to be found.
Toeplitz Lecture presented at Tel Aviv University, March, 1993
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© 1994 Birkhäuser Verlag
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Widom, H. (1994). Random Hermitian Matrices and (Nonrandom) Toeplitz Matrices. In: Basor, E.L., Gohberg, I. (eds) Toeplitz Operators and Related Topics. Operator Theory Advances and Applications, vol 71. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8543-0_2
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