Please use this identifier to cite or link to this item: `http://hdl.handle.net/2445/125123`
DC FieldValueLanguage
dc.contributor.authorArraz Almirall, Alexis-
dc.date.accessioned2018-10-08T07:59:53Z-
dc.date.available2018-10-08T07:59:53Z-
dc.date.issued2018-06-27-
dc.identifier.urihttp://hdl.handle.net/2445/125123-
dc.descriptionTreballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Joaquim Ortega Cerdàca
dc.description.abstract[en] In this project we deal with random analytic functions. Here we specifically use Gaussian analytic functions. Without technicalities, a GAF \$f\$ (for short) is a random holomorphic function on a region of \$\mathbb{C}\$ such that \$( f ( z 1 ) , ..., f ( z n ))\$ is a random vector with normal distribution. One way to generate them is using linear combinations of holomorphic functions whose coefficients are Gaussian random variables in \$\mathbb{C}\$ (or in \$\mathbb{R}\$ in special cases). For finding the zero set of a GAF we work on four isometric - invariant Hilbert spaces of analytic functions: the Fock space in \$\mathbb{C}\$, the finite space of polynomials in \$\mathbb{S}^2\$, the weighted Bergman space in \$\mathbb{D}\$ and the Paley - Wiener space. The first intensity determines the average of the distribution of the zero set of a GAF, and the Edelman - Kostlan formula gives an explicit expression of it. A result of uniqueness, called Calabi’s Rigidity, concludes that the first intensity determines the distribution of the zero set of a GAF. At the end, some examples made in C++ and gnuplot clarify the theory in these Hilbert spaces.ca
dc.format.extent81 p.-
dc.format.mimetypeapplication/pdf-
dc.language.isoengca
dc.rightscc-by-nc-nd (c) Alexis Arraz Almirall, 2018-
dc.subject.classificationFuncions de variables complexesca
dc.subject.classificationTreballs de fi de grau-
dc.subject.classificationTeoria geomètrica de funcionsca
dc.subject.classificationProcessos puntualsca
dc.subject.otherFunctions of complex variablesen
dc.subject.otherBachelor's thesis-
dc.subject.otherGeometric function theoryen
dc.subject.otherPoint processesen
dc.titleZeros of random analytic functionsca
dc.typeinfo:eu-repo/semantics/bachelorThesisca
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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