Geodesic
Random sections of convex bodies
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 190-199 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Consider a convex body $D$ in $\mathbb{R}^n$. We obtain an explicit formula expressing the distribution function of the distance between two random points uniformly and independently chosen in $D$ in terms of the distribution function of the length of a random chord of $D$. As a corollary, we derive Kingman's formula which connects the moments of these distributions. 
@article{ZNSL_2019_486_a10,
     author = {T. Moseeva},
     title = {Random sections of convex bodies},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {190--199},
     year = {2019},
     volume = {486},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a10/}
}
TY  - JOUR
AU  - T. Moseeva
TI  - Random sections of convex bodies
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2019
SP  - 190
EP  - 199
VL  - 486
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a10/
LA  - ru
ID  - ZNSL_2019_486_a10
ER  - 
%0 Journal Article
%A T. Moseeva
%T Random sections of convex bodies
%J Zapiski Nauchnykh Seminarov POMI
%D 2019
%P 190-199
%V 486
%U http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a10/
%G ru
%F ZNSL_2019_486_a10
T. Moseeva. Random sections of convex bodies. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 190-199. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a10/

[1] N. Aharonyan, V. Ohanyan, “Moments of the distance between two random points”, Model. Artif. Intell, 10:2 (2016), 64–70

[2] J. Kingman, “Random secants of a convex body”, J. Appl. Probab., 6:3 (1969), 660–672 | DOI | MR | Zbl

[3] L. Santaló, Integral Geometry and Geometric Probability, Addison-Wesley Publishing Company, 1976 | MR | Zbl

[4] R. Schneider, W. Weil, Stochastic and Integral Geometry, Springer–Verlag, 2008 | MR | Zbl