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Title: Limiting Distribution of the Complex Roots of Random Polynomials
Authors: Newman, Heather
Advisors: Nguyen, Oanh
Department: Mathematics
Class Year: 2019
Abstract: In this thesis, we follow the proof of a general result of Kabluchko and Zaporozhets in [8] about the limiting distribution of the complex roots of a (finite or infinite) random polynomial indexed by a natural number n, as n goes to infinity, when the coefficients of the polynomial satisfy certain conditions. We briefly discuss a recent and related result by Bloom and Dauvergne in [1], which gives a stronger sense of convergence for polynomials of degree n. Next, we investigate the limiting distributions for a class of polynomials considered by Schehr and Majumdar in [11], in which the asymptotics for the expected number of real roots exhibit phase transitions along a parameter \alpha. We provide a conjecture for the limiting distributions of this class, using a heuristic argument based on the methods in the result of Kabluchko and Zaporozhets, and find that, if the conjecture is correct, phase transitions occur in the limiting distributions, as well.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2020

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