On random tridiagonal matrices and the beta log-gas

Title

On random tridiagonal matrices and the beta log-gas

 Author

Breunissen, Rens (TU Delft Electrical Engineering, Mathematics and Computer Science)

Contributor

Groenevelt, Wolter (mentor)
van Elderen, Emiel (graduation committee)
Carinci, Gioia (graduation committee)

Degree granting institution

Delft University of Technology

 Programme

Applied Mathematics

 Project

Bachelor Project

 Date

2019-06-21

 Abstract

In this thesis the beta log-gas probability density function is discussed. It is shown that there is a strong link between this density function and Jacobi matrices. A change of variables exercise shows that the distribution of eigenvalues is exactly like the quadratic beta log-gas. The change of variables gives the normalization constant for the quadratic beta log-gas. Finally, it is made likely that the Jacobi matrix adheres to Wigners semicircle law, and that the beta log-gas is limited by the semicircle distribution.

 Subject

Analysis
random matrices
beta log-gas

 To reference this document use:

http://resolver.tudelft.nl/uuid:5b5c0c68-750e-43e7-b955-15b0e5603bc6

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2019 Rens Breunissen
Files
PDF BSc_thesis_Rens_Breunissen.pdf 438.06 KB
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