Book Review: Random matrix theory: invariant ensembles and universality
نویسندگان
چکیده
منابع مشابه
Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles
Abstract. We give a proof of universality in the bulk for orthogonal (β = 1) and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e (x) where V is a polynomial, V (x) = κ2mx+· · · , κ2m > 0. For such weights the associated equilibrium measure is supported on a single interval. The precise statement of our results is given in Theorem 1.1 below. F...
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which is the Central Limit Theorem. In principle, all the random variables X1, X2, · · · , XN can be of order 1, hence SN ∼ 1 as well, but the probability of having such a rare event is incredibly small. We can even estimate the bound on the probability for the rare event from the large deviation principle. A similar phenomenon happens when we form a large matrix from i.i.d. random variables an...
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The paper is devoted to the rigorous proof of the universality conjecture of the random matrix theory, according to which the limiting eigenvalue statistics of n n random matrices within spectral intervals of the order O(n ) is determined by the type of matrices (real symmetric, Hermitian or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermi...
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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 for β = 1 to the kernel of chiral Random Matrix Theories with complex matrix elements (β = 2), whic...
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We study random-matrix ensembles with a non-Gaussian probability distribution P (H) ∼ exp(−Ntr V (H)) where N is the dimension of the matrix H and V (H) is independent of N . Using Efetov’s supersymmetry formalism, we show that in the limit N → ∞ both energy level correlation functions and correlation functions of S-matrix elements are independent of P (H) and hence universal on the scale of th...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2011
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-2010-01307-0