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1. Johnson, Tobias Lee. Eigenvalue fluctuations for random regular graphs.

Degree: PhD, 2014, University of Washington

One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random regular graphs. Specifically, we prove limit theorems for the fluctuations of linear spectral statistics of random regular graphs. We find both universal and non-universal behavior. Our most important tool is Stein's method for Poisson approximation, which we develop for use on random regular graphs. Advisors/Committee Members: Dumitriu, Ioana (advisor).

Subjects/Keywords: corners process; eigenvalue fluctuations; minors process; Poisson approximation; random regular graphs; Stein's method; Mathematics; mathematics

…In Chapter 4, we consider a process of growing random regular graphs. The eigenvalue… …fluctuations are then a stochastic process whose marginals are given by the results of Chapter 3… …This is analogous to a corners process in random matrix theory; see [BG13] for a… …minors of an infinite random matrix. One can then consider not just the marginal distribution… …matrix and its minors. The limiting fluctuations of some of these processes can be expressed in… 

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APA (6th Edition):

Johnson, T. L. (2014). Eigenvalue fluctuations for random regular graphs. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/26531

Chicago Manual of Style (16th Edition):

Johnson, Tobias Lee. “Eigenvalue fluctuations for random regular graphs.” 2014. Doctoral Dissertation, University of Washington. Accessed July 11, 2020. http://hdl.handle.net/1773/26531.

MLA Handbook (7th Edition):

Johnson, Tobias Lee. “Eigenvalue fluctuations for random regular graphs.” 2014. Web. 11 Jul 2020.

Vancouver:

Johnson TL. Eigenvalue fluctuations for random regular graphs. [Internet] [Doctoral dissertation]. University of Washington; 2014. [cited 2020 Jul 11]. Available from: http://hdl.handle.net/1773/26531.

Council of Science Editors:

Johnson TL. Eigenvalue fluctuations for random regular graphs. [Doctoral Dissertation]. University of Washington; 2014. Available from: http://hdl.handle.net/1773/26531

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