Statistics of real roots of random polynomials

Bojnik, Afrim (2019) Statistics of real roots of random polynomials. [Thesis]

[thumbnail of 10278991_AfrimBojnik.pdf] PDF
10278991_AfrimBojnik.pdf

Download (874kB)

Abstract

In this thesis, we present two approaches in order to study the expected number of real zeros of random univariate polynomials. Namely, the Kac-Rice method and Edelman-Kostlan's geometric approach. We derive a remarkable result called the Kac-Rice formula concerning the expected number of real zeros and apply this result to certain random polynomial ensembles. We also report some basic facts from potential theory in the complex plane and its connection to complex random polynomials. In addition, we consider certain random orthogonal polynomials associated to suitable weight functions supported in the complex plane, and we present some known results in this direction
Item Type: Thesis
Uncontrolled Keywords: Random polynomials. -- Kac-Rice formula. -- Potential theory. -- Bergman kernel asymptotics. -- Rassal polinomlar. -- Kac-Rice formülü. -- Potansiyel teori. -- Bergman çekirdek asimptotikleri.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 26 Sep 2019 10:50
Last Modified: 26 Apr 2022 10:31
URI: https://research.sabanciuniv.edu/id/eprint/39264

Actions (login required)

View Item
View Item