No description available.

This thesis consists of two parts, Papers A and B, in which some stochastic processes, originating from random matrix theory (RMT), are studied. In the first paper we study the fluctuations of the kth largest eigenvalue, xk, of the Gaussian unitary ensemble (GUE). That is, let N be the dimension of the matrix and k depend on N in such a way that k and N-k both tend to infinity as N - ∞. The main result is that xk, when appropriately rescaled, converges in distribution to a Gaussian random variable as N → ∞. Furthermore, if k1 < ...< km are such that k1, ki+1 - ki and N - km, i =1, ... ,m - 1, tend to infinity as N → ∞ it is shown that (xk1 , ... , xkm) is multivariate Gaussian in the rescaled N → ∞ limit. In the second paper we study the Airy process, A(t), and prove that it fluctuates like a Brownian motion on a local scale. We also prove that the Discrete polynuclear growth process (PNG) fluctuates like a Brownian motion in a scaling limit smaller than the one where one gets the Airy process. / QC 20100716

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, December 2003. / Includes bibliographical references. Also available on the Internet.

published_or_final_version / Statistics / Master / Master of Philosophy

No description available.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 170-182).

Thesis (D.Com.(Financial Management Sciences))--University of Pretoria, 2009. / Abstract in English. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 121-123).

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 68-69).