On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles
نویسندگان
چکیده
منابع مشابه
Spectral Universality of Real Chiral Random Matrix Ensembles
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...
متن کاملSpectral Universality for Real Chiral Random Matrix Ensembles
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...
متن کاملUniversality 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...
متن کاملUniversality of random-matrix results for non-Gaussian ensembles.
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...
متن کاملOn the Proof of Universality for Orthogonal and Symplectic Ensembles in Random Matrix Theory
We give a streamlined proof of a quantitative version of a result from [DG1] which is crucial for the proof of universality in the bulk [DG1] and also at the edge [DG2] for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the β = 1, 2, 4 partition functions for log gases.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2002
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-002-0711-6