Geodesic
Estimates of the concentration functions of weighted sums of independent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 768-777

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X_1,\dots,X_n$ be independent and identially distributed random variables. The paper deals with obtaining upper bounds on the concentration function of the weighted sums $\sum_{k=1}^na_kX_k$ based on the coefficients $a_k$, $1\leqslant k\leqslant n$. Results obtained in this paper improve over the recent works in [O. Friedland and S. Sodin, C. R., Math., Acad. Sci. Paris 345, No. 9, 513–518 (2007; Zbl 1138.60023)] and [M. Rudelson and R. Vershynin, Adv. Math. 218, No. 2, 600–633 (2008; Zbl 1139.15015), Commun. Pure Appl. Math. 62, No. 12, 1707–1739 (2009; Zbl 1183.15031)].
Keywords: concentration functions; inequalities; sums of independent random variables; Littlewood–Offord problem. 
@article{TVP_2012_57_4_a8,
     author = {Yu. S. Eliseeva and A. Yu. Zaitsev},
     title = {Estimates of the concentration functions of weighted sums of independent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {768--777},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a8/}
}
TY  - JOUR
AU  - Yu. S. Eliseeva
AU  - A. Yu. Zaitsev
TI  - Estimates of the concentration functions of weighted sums of independent random variables
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2012
SP  - 768
EP  - 777
VL  - 57
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a8/
LA  - ru
ID  - TVP_2012_57_4_a8
ER  - 
%0 Journal Article
%A Yu. S. Eliseeva
%A A. Yu. Zaitsev
%T Estimates of the concentration functions of weighted sums of independent random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2012
%P 768-777
%V 57
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a8/
%G ru
%F TVP_2012_57_4_a8
Yu. S. Eliseeva; A. Yu. Zaitsev. Estimates of the concentration functions of weighted sums of independent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 768-777. http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a8/