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Title: Zero sets of gaussian analytic functions
Author: Morgó Homs, Joan
Director/Tutor: Massaneda Clares, Francesc Xavier
Keywords: Funcions analítiques
Treballs de fi de grau
Corbes el·líptiques
Varietats abelianes
Funcions zeta
Processos gaussians
Funcions enteres
Analytic functions
Bachelor's theses
Elliptic curves
Abelian varieties
Zeta functions
Gaussian processes
Entire functions
Issue Date: 18-Jan-2019
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 cases.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Francesc Xavier Massaneda Clares
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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