Massaneda Clares, Francesc Xavierde la Calle Vicente, Guillem2022-04-192022-04-192021-06-20https://hdl.handle.net/2445/184995Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Francesc Xavier Massaneda Clares[en] In this project we deal with random holomorphic polynomials $p_{N}$. Specifically, we study the relationship between zeros and critical points of $p_{N}$ considering two different probabilistic models. The first one is based on chosing independently and with uniform probability $N$ random points that will be the zeros of our polynomial $p_{N}$. The second model is that of the so-called parabolic Gaussian Analytic Function. In this second model, the distribution of points is more rigid, and the striking phenomenon continues to be observed: zeros and critical points appear, with high probability, in pairs.57 p.application/pdfengcc-by-nc-nd (c) Guillem de la Calle Vicente, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Funcions de variables complexesTreballs de fi de grauTeoria geomètrica de funcionsProcessos estocàsticsPolinomisFunctions of complex variablesBachelor's thesesGeometric function theoryStochastic processesPolynomialsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess