Real symmetric random matrices and replicas.
نویسندگان
چکیده
Various ensembles of random matrices with independent entries are analyzed by the replica formalism in the large- N limit. A result on the Laplacian random matrix with Wigner-rescaling is generalized to arbitrary probability distribution.
منابع مشابه
No-gaps Delocalization for General Random Matrices
We prove that with high probability, every eigenvector of a random matrix is delocalized in the sense that any subset of its coordinates carries a non-negligible portion of its `2 norm. Our results pertain to a wide class of random matrices, including matrices with independent entries, symmetric and skew-symmetric matrices, as well as some other naturally arising ensembles. The matrices can be ...
متن کاملSpectral statistics for ensembles of various real random matrices
We investigate spacing statistics for ensembles of various real random matrices where the matrixelements have various Probability Distribution Function (PDF: f(x)) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derived that spacing distribution p(s) of adjacent energy eigenvalues are distinct. Nevertheless, they show the linear level repulsion near s = 0 as αs...
متن کاملPoisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles
The two archetypal ensembles of random matrices are Wigner real symmetric (Hermitian) random matrices and Wishart sample covariance real (complex) random matrices. In this paper we study the statistical properties of the largest eigenvalues of such matrices in the case when the second moments of matrix entries are infinite. In the first two subsections we consider Wigner ensemble of random matr...
متن کاملLimit Distributions for Random Hankel, Toeplitz Matrices and Independent Products
For random selfadjoint (real symmetric, complex Hermitian, or quaternion self-dual) Toeplitz matrices and real symmetric Hankel matrices, the existence of universal limit distributions for eigenvalues and products of several independent matrices is proved. The joint moments are the integral sums related to certain pair partitions. Our method can apply to random Hankel and Toeplitz band matrices...
متن کاملBetti numbers of random real hypersurfaces and determinants of random symmetric matrices
We asymptotically estimate from above the expected Betti numbers of random real hypersurfaces in smooth real projective manifolds. Our upper bounds grow as the square root of the degree of the hypersurfaces as the latter grows to infinity, with a coefficient involving the Kählerian volume of the real locus of the manifold as well as the expected determinant of random real symmetric matrices of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 74 5 Pt 1 شماره
صفحات -
تاریخ انتشار 2006