Transportation to random zeroes by the gradient flow

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dc.creatorNazarov, Fedor
dc.creatorSodin, Mikhail
dc.creatorVolberg, Alexander
dc.date2005-10-30
dc.date2007-03-05
dc.date.accessioned2026-07-07T07:49:52Z
dc.date.available2026-07-07T07:49:52Z
dc.descriptionWe consider the zeroes of a random Gaussian Entire Function f and show that their basins under the gradient flow of the random potential U partition the complex plane into domains of equal area. We find three characteristic exponents 1, 8/5, and 4 of this random partition: the probability that the diameter of a particular basin is greater than R is exponentially small in R; the probability that a given point z lies at a distance larger than R from the zero it is attracted to decays as exp(-R^{8/5}); and the probability that, after throwing away 1% of the area of the basin, its diameter is still larger than R decays as exp(-R^4). We also introduce a combinatorial procedure that modifies a small portion of each basin in such a way that the probability that the diameter of a particular modified basin is greater than R decays only slightly slower than exp(-cR^4).
dc.descriptionImprovement of presentation in sections 4 and 11, tiny changes in other sections
dc.identifierhttps://arxiv.org/abs/math/0510654
dc.identifierhttp://arxiv.org/abs/math/0510654
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124979
dc.subjectComplex Variables
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject30B20, 30C15, 60G60
dc.titleTransportation to random zeroes by the gradient flow
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