Graph diameter in long-range percolation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F11%3A43878883" target="_blank" >RIV/60076658:12510/11:43878883 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/rsa.20349" target="_blank" >http://dx.doi.org/10.1002/rsa.20349</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/rsa.20349" target="_blank" >10.1002/rsa.20349</a>

Result language
angličtina
Original language name
Graph diameter in long-range percolation
Original language description
We study the asymptotic growth of the diameter of a graph obtained by adding sparse "long" edges to a square box in Zd. We focus on the cases when an edge between x and y is added with probability decaying with the Euclidean distance as |x ? y|^{?s}+o(1)when |x ? y| ? oo. For s in the interval (d, 2d) we show that the graph diameter for the graph reduced to a box of side L scales like (log L)^{?+o(1)} where ?^{-1} := log_2(2d/s). In particular, the diameter grows about as fast as the typical graph distance between two vertices at distance L. We also show that a ball of radius r in the intrinsic metric on the (infinite) graph will roughly coincide with a ball of radius exp{r^{1/?}+o(1)} in the Euclidean metric.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)