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dc.contributor.advisorMassaneda Clares, Francesc Xavier-
dc.contributor.authorMorgó Homs, Joan-
dc.descriptionTreballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Francesc Xavier Massaneda Claresca
dc.description.abstract[en] We study point processes given as zero sets of Gaussian analytic functions and prove that these point processes show local repulsion. We define Gaussian analytic functions and introduce its covariance kernel, which determines its probabilistic properties, and its first intensity which can be computed using the Edelman-Kostlan formula. Finally, we also study rigidness of some model examples -by computing the variance of the counting random variable of the zeros of the GAF- and we compare it with the independence of the Poisson point process -shown in an introductory section of this project- for the same model
dc.format.extent35 p.-
dc.rightscc-by-nc-nd (c) Joan Morgó Homs, 2019-
dc.subject.classificationFuncions analítiquesca
dc.subject.classificationTreballs de fi de grau-
dc.subject.classificationCorbes el·líptiquesca
dc.subject.classificationVarietats abelianesca
dc.subject.classificationFuncions zetaca
dc.subject.classificationProcessos gaussiansca
dc.subject.classificationFuncions enteresca
dc.subject.otherAnalytic functionsen
dc.subject.otherBachelor's thesis-
dc.subject.otherElliptic curvesen
dc.subject.otherAbelian varietiesen
dc.subject.otherZeta functionsen
dc.subject.otherGaussian processesen
dc.subject.otherEntire functionsen
dc.titleZero sets of gaussian analytic functionsca
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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