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

Voir la notice de l'article 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). 
@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},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--137},
     publisher = {mathdoc},
     volume = {412},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a6/}
}
TY  - JOUR
AU  - Yu. S. Eliseeva
TI  - Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 121
EP  - 137
VL  - 412
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a6/
LA  - ru
ID  - ZNSL_2013_412_a6
ER  - 
%0 Journal Article
%A Yu. S. Eliseeva
%T Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 121-137
%V 412
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a6/
%G ru
%F ZNSL_2013_412_a6
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/