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Developments in random matrix theory
 J. Phys. A: Math. Gen
, 2000
"... In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given. 1 1 ..."
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In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given. 1 1
Random matrix theory
, 2005
"... Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We includ ..."
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Cited by 80 (4 self)
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Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We
RANDOM MATRIX THEORY
"... Random matrix theory is usually taught as a sequence of several graduate courses; we have 16 lectures, so we will give a very brief introduction. Some relevant books for the course: • G. Anderson, A. Guionnet, O. Zeitouni. An introduction to random matrices. [1] ..."
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Random matrix theory is usually taught as a sequence of several graduate courses; we have 16 lectures, so we will give a very brief introduction. Some relevant books for the course: • G. Anderson, A. Guionnet, O. Zeitouni. An introduction to random matrices. [1]
Riemann zeros and random matrix theory
, 2009
"... In the past dozen years random matrix theory has become a useful tool for conjecturing answers to old and important questions in number theory. It was through the Riemann zeta function that the connection with random matrix theory was first made in the 1970s, and although there has also been much re ..."
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Cited by 4 (0 self)
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In the past dozen years random matrix theory has become a useful tool for conjecturing answers to old and important questions in number theory. It was through the Riemann zeta function that the connection with random matrix theory was first made in the 1970s, and although there has also been much
Random Matrix Theory and ζ(1/2 + it)
, 2000
"... We study the characteristic polynomials Z(U,#)of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the moments of and Z/Z # , and from these we obtain the asymptotics of the value distributions and cumulants of the re ..."
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Cited by 161 (20 self)
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We study the characteristic polynomials Z(U,#)of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the moments of and Z/Z # , and from these we obtain the asymptotics of the value distributions and cumulants
THE SHANNON TRANSFORM IN RANDOM MATRIX THEORY
"... and Pastur (1967), were motivated to a large extent by their applications. In this paper we report on a new transform motivated by the application of random matrices to various problems in the information theory of noisy communication channels. The Shannon transform of a nonnegative random variable ..."
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X is defined as VX(γ) = E[log(1 + γX)]. (1) where γ is a nonnegative real number. Originally introduced in [12], its applications to random matrix theory and engineering applications have been developed in [3]. In this paper we give a summary of its main properties and applications in random
Random Matrix Theory
, 2005
"... Abstract. We investigate random, discrete Schrödiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson’s Coulomb gas inverse temperature β. They belong to the class of “critical ” random 1 − Schrödiner operators with random potentials which diminish ..."
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Abstract. We investigate random, discrete Schrödiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson’s Coulomb gas inverse temperature β. They belong to the class of “critical ” random 1 − Schrödiner operators with random potentials which
Hypothesis Testing and Random Matrix Theory
"... Abstract—Detection of the number of signals embedded in noise is a fundamental problem in signal and array processing. This paper focuses on the nonparametric setting where no knowledge of the array manifold is assumed. First, we present a detailed statistical analysis of this problem, including an ..."
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an analysis of the signal strength required for detection with high probability, and the form of the optimal detection test under certain conditions where such a test exists. Second, combining this analysis with recent results from random matrix theory, we present a new algorithm for detection of the number
Results 1  10
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1,851,454