Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 466-481
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G. О. H. Katona. Inequalities for the distribution of the length of random vector sums. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 466-481. http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a1/
@article{TVP_1977_22_3_a1,
author = {G. {\CYRO}. H. Katona},
title = {Inequalities for the distribution of the length of random vector sums},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {466--481},
year = {1977},
volume = {22},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a1/}
}
TY - JOUR
AU - G. О. H. Katona
TI - Inequalities for the distribution of the length of random vector sums
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1977
SP - 466
EP - 481
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a1/
LA - ru
ID - TVP_1977_22_3_a1
ER -
%0 Journal Article
%A G. О. H. Katona
%T Inequalities for the distribution of the length of random vector sums
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1977
%P 466-481
%V 22
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a1/
%G ru
%F TVP_1977_22_3_a1
Starting from a combinatorial proof of the inequality $$ \mathbf P(|\xi+\eta|\ge x)\ge\frac{1}{2}\mathbf P^2(|\xi|\ge x). $$ where $\xi$ and $\eta$ are independent random vectors in a $d$-dimensional Euclidean space, continuous analogues of the combinatorial model are constructed, which enable to deduce inequalities similar to the above.
