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http://hdl.handle.net/2445/184995
Title: | Pairing of zeros and critical points for random polynomials |
Author: | de la Calle Vicente, Guillem |
Director/Tutor: | Massaneda Clares, Francesc Xavier |
Keywords: | Funcions de variables complexes Treballs de fi de grau Teoria geomètrica de funcions Processos estocàstics Polinomis Functions of complex variables Bachelor's theses Geometric function theory Stochastic processes Polynomials |
Issue Date: | 20-Jun-2021 |
Abstract: | [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. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Francesc Xavier Massaneda Clares |
URI: | http://hdl.handle.net/2445/184995 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_guillem_de_la_calle.pdf | Memòria | 1.61 MB | Adobe PDF | View/Open |
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