On the Law of Addition of Random Matrices
نویسنده
چکیده
Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices An and Bn rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix Un (i.e. An + U∗ nBnUn) is studied in the limit of large matrix order n. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the Stieltjes transform of the limiting measure in terms of limiting eigenvalue measures of An and Bn is obtained and studied.
منابع مشابه
Effect of Composition on Release of Aroma Compounds
The effect of oleic acid (5 and 10% v/v) and xanthan gum (0.5 and 1% wt) on partitioning and retention of ethyl acetate and diacetyl from two matrices with a different composition was investigated by applying static head space gas chromatography. Two matrices with different composition have been developed: one containing carbohydrates (xanthan gum) and in the second one, called co...
متن کاملMARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES
In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let be a double sequence of pairwise negatively dependent random variables. If for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). In addition, it also converges to 0 in ....
متن کاملMore about measures and Jacobians of singular random matrices
In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
متن کاملComparative Study of Random Matrices Capability in Uncertainty Detection of Pier’s Dynamics
Because of random nature of many dependent variables in coastal engineering, treatment of effective parameters is generally associated with uncertainty. Numerical models are often used for dynamic analysis of complex structures, including mechanical systems. Furthermore, deterministic models are not sufficient for exact anticipation of structure’s dynamic response, but probabilistic models...
متن کاملON SELBERG-TYPE SQUARE MATRICES INTEGRALS
In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.
متن کاملOn the Convergence Rate of the Law of Large Numbers for Sums of Dependent Random Variables
In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.
متن کامل