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Title:  The circular law: Proof of the replacement principle 
Authors:  Tang, ZHIWEI 

Keywords:  random matrices, semicircle law, circular law conjecture emprical spectral distribution, Stieltjes transform 
Issue Date:  2009 
Series/Report no.:  Canadian theses 
Abstract:  It was conjectured in the early 1950¡¯s that the empirical
spectral distribution (ESD) of an $n \times n$ matrix whose entries
are independent and identically distributed with mean zero and
variance one, normalized by a factor of $\frac{1}{\sqrt{n}}$,
converges to the uniform distribution over the unit disk on the
complex plane, which is called the circular law. The goal of this
thesis is to prove the so called Replacement Principle introduced by
Tao and Vu which is a crucial step in their recent proof of the
circular law in full generality. It gives a general criterion for
the difference of the ESDs of two normalised random matrices
$\frac{1}{\sqrt{n}}A_n$, $\frac{1}{\sqrt{n}}B_n$ to converge to 0. 
Description:  Thesis (Master, Mathematics & Statistics)  Queen's University, 20090711 14:57:44.225 
URI:  http://hdl.handle.net/1974/1985 
Appears in Collections:  Queen's Graduate Theses and Dissertations Department of Mathematics and Statistics Graduate Theses

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