Correlations between zeros of non-Gaussian random polynomials

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dc.creatorBleher, Pavel M.
dc.creatorDi, Xiaojun
dc.date2003-08-11
dc.date.accessioned2026-07-07T04:30:27Z
dc.date.available2026-07-07T04:30:27Z
dc.descriptionThe existence of the scaling limit and its universality, for correlations between zeros of {\it Gaussian} random polynomials, or more generally, {\it Gaussian} random sections of powers of a line bundle over a compact manifold has been proved in a great generality in the works [BBL2], [Ha], [BD], [BSZ1]-[BSZ4], and others. In the present work we prove the existence of the scaling limit for a class of {\it non-Gaussian} random polynomials. Our main result is that away from the origin the scaling limit exists and is universal, so that it does not depend on the distribution of the coefficients. At the origin the scaling limit is not universal, and we find a crossover from the nonuniversal asymptotics of the density of the probability distribution of zeros at the origin to the universal one away from the origin.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0308014
dc.identifierhttp://arxiv.org/abs/math-ph/0308014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57470
dc.subjectMathematical Physics
dc.subject60D05
dc.titleCorrelations between zeros of non-Gaussian random polynomials
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