[Colloquium] Zelin Lv MS Presentation/May 10, 2023

[Megan Woodward]

This is an announcement of Zelin Lv's MS Presentation
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Candidate: Zelin Lv

Date: Wednesday, May 10, 2023

Time:  3 pm CST

Remote Location: Meeting ID: 979 2663 7869. Passcode: 430720

Location: JCL 390

M.S. Paper Title: On the Moments of Random Determinants

Abstract: This thesis investigates the moments of random determinants, specifically focusing on the second, fourth, and sixth moments of determinants of random matrices. The study of random determinants and their moments has been an active area of research. Building on the existing literature, we provide an in-depth analysis of these moments, offering new insights into their properties and behavior.

Additionally, we introduce a novel approach to compute the determinant of the second moment of determinants of symmetric random matrices. This new method has the potential to contribute to the development of computing higher moments of determinants of random matrices.

The main contributions of this thesis are: a comprehensive analysis of the second, fourth, and sixth moments of random determinants by applying the existing techniques in an in- tricate way and the proposal of a new and simple approach for computing the determinant of the determinants of symmetric random matrices, with an application of computing the second moment. This work not only advances our understanding of the moments of random determinants but also presents potential avenues for further exploration in random matrix theory.

Advisors: Aaron Potechin

Committee Members: Janos Simon, Aaron Potechin, and Alexander Razborov


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