Spectral Analysis of Random Sparse Matrices
نویسندگان
چکیده
منابع مشابه
Spectral Analysis of Random Sparse Matrices
We study n×n random symmetric matrices whose entries above the diagonal are iid random variables each of which takes 1 with probability p and 0 with probability 1 − p, for a given density parameter p = α/n for sufficiently large α. For a given such matrix A, we consider a matrix A′ that is obtained by removing some rows and corresponding columns with too many value 1 entries. Then for this A′, ...
متن کاملSpectral radii of sparse random matrices
We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erdős-Rényi graphs. For the Erdős-Rényi graph G(n, d/n), our results imply that the smallest and second-largest eigenvalues of the adjacency matrix converge to the edges of the support of the asymptotic eigenvalue distribution provided that d log n. Toget...
متن کاملSpectra of sparse random matrices
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica. Our formulation of the replica-symmetric ansatz shares the symmetries of the one suggested in a seminal paper by Rodgers and Bray (symmetry with respect to permutation of replica and rotation symmetry in the space of replica), but uses a different representation in terms of superpositions of Gaus...
متن کاملSparse Recovery Using Sparse Random Matrices
Over the recent years, a new *linear* method for compressing high-dimensional data (e.g., images) has been discovered. For any high-dimensional vector x, its *sketch* is equal to Ax, where A is an m x n matrix (possibly chosen at random). Although typically the sketch length m is much smaller than the number of dimensions n, the sketch contains enough information to recover an *approximation* t...
متن کاملSpectral Density of Sparse Sample Covariance Matrices
Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form J = ATA, where A is an M × N real sparse random matrix. The difference from a dense random matrix is the most significant in the tail region of the spectrum. We compare the results of several approximation schemes, focusing on the behavior in...
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: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
سال: 2011
ISSN: 0916-8508,1745-1337
DOI: 10.1587/transfun.e94.a.1247