Geodesic
A~strong law of large numbers for random biased connected graphs
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 344-354

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

We consider a class of random connected graphs with random vertices and random edges in which the randomness of the vertices is determined by a continuous probability distribution and the randomness of the edges is determined by a connection function. We derive a strong law of large numbers on the total lengths of all random edges for a random biased connected graph that is a generalization of a directed $k$-nearest-neighbor graph.
Keywords: random connected graph, random biased connected graph, law of large numbers. 
@article{TMF_2012_172_3_a1,
     author = {Zhonghao Xu and Ya. Higuchi and Chunhua},
     title = {A~strong law of large numbers for random biased connected graphs},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {344--354},
     publisher = {mathdoc},
     volume = {172},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a1/}
}
TY  - JOUR
AU  - Zhonghao Xu
AU  - Ya. Higuchi
AU  - Chunhua
TI  - A~strong law of large numbers for random biased connected graphs
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 344
EP  - 354
VL  - 172
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a1/
LA  - ru
ID  - TMF_2012_172_3_a1
ER  - 
%0 Journal Article
%A Zhonghao Xu
%A Ya. Higuchi
%A Chunhua
%T A~strong law of large numbers for random biased connected graphs
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 344-354
%V 172
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a1/
%G ru
%F TMF_2012_172_3_a1
Zhonghao Xu; Ya. Higuchi; Chunhua. A~strong law of large numbers for random biased connected graphs. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 344-354. http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a1/