Massaneda Clares, Francesc XavierMorgó Homs, Joan2019-09-192019-09-192019-01-18https://hdl.handle.net/2445/140519Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Francesc Xavier Massaneda Clares[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 cases.35 p.application/pdfengcc-by-nc-nd (c) Joan Morgó Homs, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/es/Funcions analítiquesTreballs de fi de grauCorbes el·líptiquesVarietats abelianesFuncions zetaProcessos gaussiansFuncions enteresAnalytic functionsBachelor's thesesElliptic curvesAbelian varietiesZeta functionsGaussian processesEntire functionsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess