Dissertation/Thesis Abstract

The Central Limit Theorem for Linear Spectral Statistics of Submatrices of the Gaussian Wigner Random Matrices
by Reed, Matthew, Ph.D., University of California, Davis, 2014, 123; 3646379
Abstract (Summary)

The main topic addressed here is the joint distribution of spectra of submatrices M(1) and M(2) of large Gaussian Wigner matrices M. A multidimensional central limit theorem for linear statistics of the eigenvalues of submatrices will be proved with explicit formulas for the covariance that relate the spectra to a random surface model known as the Gaussian free field. The regularity assumption is that test functions belong to the Sobolev space H s, for s > 5/2.

The organization is as follows. Chapters 1 and 2 consist of an introduction to Wigner matrices and the central limit theorem in the random matrix theory. Chapter 3 is a discussion of the results which motivated this work, in addition to an introduction to the Gaussian free field. Chapter 4 contains the new results of the author, and chapter 5 is an appendix describing some technical tools.

Indexing (document details)
Advisor: Soshnikov, Alexander
Commitee: Gravner, Janko, Tracy, Craig
School: University of California, Davis
Department: Mathematics
School Location: United States -- California
Source: DAI-B 76/04(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Central, Eigenvalues, Limit, Matrix, Theorem, Wigner
Publication Number: 3646379
ISBN: 9781321363777