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tfg_guillem_de_la_calle.pdf (1.57 MB)

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Bachelor thesis

Publication date

2021-06-20

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cc-by-nc-nd (c) Guillem de la Calle Vicente, 2021
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/184995

Pairing of zeros and critical points for random polynomials

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Francesc Xavier Massaneda Clares

Subject

Funcions de variables complexes, Treballs de fi de grau, Teoria geomètrica de funcions, Processos estocàstics, Polinomis

Subject (English)

Functions of complex variables, Bachelor's theses, Geometric function theory, Stochastic processes, Polynomials

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

DE LA CALLE VICENTE, Guillem. Pairing of zeros and critical points for random polynomials. [consulted: 9 of August of 2026]. Available at: https://hdl.handle.net/2445/184995

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