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.
|Commitee:||Gravner, Janko, Tracy, Craig|
|School:||University of California, Davis|
|School Location:||United States -- California|
|Source:||DAI-B 76/04(E), Dissertation Abstracts International|
|Keywords:||Central, Eigenvalues, Limit, Matrix, Theorem, Wigner|
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