Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices

Christopher Hammond; Steven J. Miller

doi:10.1007/s10959-005-3518-5

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Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices

Christopher Hammond·Steven J. Miller

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Abstract

Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues) converges weakly to a new universal distribution with unbounded support, independent of p. This distribution's moments are almost those of the Gaussian's; the deficit may be interpreted in terms of Diophantine obstructions. With a little more work, we obtain almost sure convergence. An investigation of spacings between adjacent normalized eigenvalues looks Poissonian, and not GOE.

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BibTeX RIS

Christopher Hammond, Steven J. Miller. 2003-12-10. Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices. https://doi.org/10.1007/s10959-005-3518-5

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