The Tracy–Widom Law for Some Sparse Random Matrices
نویسندگان
چکیده
منابع مشابه
The Tracy–Widom law for some sparse random matrices
Consider the random matrix obtained from the adjacency matrix of a random d-regular graph by multiplying every entry by a random sign. The largest eigenvalue converges, after proper scaling, to the Tracy–Widom distribution.
متن کاملThe Circular Law for Random Matrices
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries. We assume that the entries have a finite moment of order large...
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 کاملLocal Circular Law for Random Matrices
The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point z away from the unit circle. More precisely, if ||z| − 1| > τ for arbitrarily small τ > 0, the circular law is valid around z up to scale N−1/2+ε for any ε > 0 under the assu...
متن کاملCircular Law Theorem for Random Markov Matrices
Let (Xjk)jk>1 be i.i.d. nonnegative random variables with bounded density, mean m, and finite positive variance σ. Let M be the n × n random Markov matrix with i.i.d. rows defined by Mjk = Xjk/(Xj1+ · · ·+Xjn). In particular, when X11 follows an exponential law, the random matrix M belongs to the Dirichlet Markov Ensemble of random stochastic matrices. Let λ1, . . . , λn be the eigenvalues 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
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2009
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-009-9813-2