On random tridiagonal matrices and the beta log-gas
Rens Breunissen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Wolter Groenevelt – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Emiel van Elderen – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Gioia Carinci – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
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.