Eigenvalue Statistics for CMV Matrices: From Poisson to Clock via Circular Beta Ensembles

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dc.creatorKillip, Rowan
dc.creatorStoiciu, Mihai
dc.date2006-07-31
dc.date.accessioned2026-07-07T07:20:35Z
dc.date.available2026-07-07T07:20:35Z
dc.descriptionWe study CMV matrices (a discrete one-dimensional Dirac-type operator) with random decaying coefficients. Under mild assumptions we identify the local eigenvalue statistics in the natural scaling limit. For rapidly decreasing coefficients, the eigenvalues have rigid spacing (like the numerals on a clock); in the case of slow decrease, the eigenvalues are distributed according to a Poisson process. For a certain critical rate of decay we obtain the circular beta ensembles of random matrix theory. The temperature β^{-1} appears as the square of the coupling constant.
dc.identifierhttps://arxiv.org/abs/math-ph/0608002
dc.identifierhttp://arxiv.org/abs/math-ph/0608002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115002
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject34B05, 42C05
dc.titleEigenvalue Statistics for CMV Matrices: From Poisson to Clock via Circular Beta Ensembles
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