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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
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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Cited by 26 (0 self)
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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
Autocorrelation of random matrix polynomials
 COMMUN. MATH. PHYS
, 2003
"... We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in t ..."
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Cited by 39 (21 self)
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in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than largematrix asymptotic
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
Random Matrix Ensembles
, 2000
"... We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories (β = 1) by relating the kernel of the correlations functions fo ..."
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We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories (β = 1) by relating the kernel of the correlations functions
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]
Random Matrix Equations
"... Let ξ be a random variable with density function w(x) supported on S. Consider the random matrix equations A(ξ)u(ξ) = f(ξ) where A(ξ) is bounded and positive definite, and f ∈ L2w (S). NOTE: It is nontrivial to guarantee that A is bounded and positive definite with Gaussian ξ. The solution often d ..."
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Let ξ be a random variable with density function w(x) supported on S. Consider the random matrix equations A(ξ)u(ξ) = f(ξ) where A(ξ) is bounded and positive definite, and f ∈ L2w (S). NOTE: It is nontrivial to guarantee that A is bounded and positive definite with Gaussian ξ. The solution often
Randomized Matrix Computations
, 2012
"... We propose new effective randomized algorithms for some fundamental matrix computations such as preconditioning of an ill conditioned matrix that has a small numerical nullity or rank, its 2by2 block triangulation, numerical stabilization of Gaussian elimination with no pivoting, and approximation ..."
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Cited by 52 (6 self)
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We propose new effective randomized algorithms for some fundamental matrix computations such as preconditioning of an ill conditioned matrix that has a small numerical nullity or rank, its 2by2 block triangulation, numerical stabilization of Gaussian elimination with no pivoting
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 522 (5 self)
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distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly
Results 1  10
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