Skip navigation
Please use this identifier to cite or link to this item:
Title: Characteristic Polynomials over Random Matrix Ensembles through a Grassman Integration Approach
Authors: Mong, Arnold
Advisors: Shcherbina, Tatyana
Department: Mathematics
Class Year: 2020
Abstract: We introduce Grassman integration to derive the asymptotic behavior of the correlation function of the product of two characteristic polynomials for various matrix ensembles. We first derive the result for the Gaussian Unitary and Gaussian Orthogonal ensembles (GUE and GOE), before moving onto general real symmetric Wigner matrices. The main result is to show that a Grassman integration approach can be used to derive a GOE universality result for second order correlation functions. While the resulting asymptotics are already known, it is unclear how to generalize any previous approach to study universality of higher order correlations. This work yields the same result for the second order correlations, and previous work on GUE universality suggests that the method can be generalized to higher order correlations over GOE as well.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2020

Files in This Item:
File Description SizeFormat 
MONG-ARNOLD-THESIS.pdf360.46 kBAdobe PDF    Request a copy

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.