Geodesic
Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 121-137 
Yu. S. Eliseeva. Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 121-137. http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a6/
@article{ZNSL_2013_412_a6,
     author = {Yu. S. Eliseeva},
     title = {Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables},
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     year = {2013},
     volume = {412},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

This article is a multidimensional generalization of the results Eliseeva and Zaitsev (2012). Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum_{k=1}^na_kX_k$ 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 some refinements of the results Friedland and Sodin (2007) and Rudelson and Vershynin (2009).

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