Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables

2013/03/16 by Eliseeva, Yu. S.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1303.4005

Abstract

Let X,X₁,…,X_n be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable ∑_k=1ⁿX_k a_k according to the arithmetic structure of vectors a_k. Recently, the interest to this question has increased significantly due to the study of distributions of eigenvalues of random matrices. In this paper we formulate and prove multidimensional generalizations of the results Eliseeva and Zaitsev (2012). They are also the refinements of the results of Friedland and Sodin (2007) and Rudelson and Vershynin (2009).

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