Gibbs random graphs on point processes

Authors
Ferrari, Pablo Augusto; Pechersky, Eugene A.; Sisko, Valentin V.; Yambartsev, Anatoly
Publication Year
2010
Language
English
Format
article
Status
Published version
Description
Consider a discrete locally finite subset G of Rd and the complete graph (G, E), with vertices G and edges E. We consider Gibbs measures on the set of sub-graphs with vertices G and edges E´ ⊂ E. The Gibbs interaction acts between open edges having a vertex in common. We study percolation properties of the Gibbs distribution of the graph ensemble. The main results concern percolation properties of the open edges in two cases: (a) when G is sampled from a homogeneous Poisson process; and (b) for a fixed G with sufficiently sparse points.

Fil: Ferrari, Pablo Augusto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Pechersky, Eugene A.. Russian Academy of Sciences. Dobrushin Laboratory of Institute for Information Transmission Problems; Rusia
Fil: Sisko, Valentin V.. Universidade Federal Fluminense; Brasil
Fil: Yambartsev, Anatoly. Universidade de Sao Paulo; Brasil
Subject
Gibbs measures
Random graphs
Point processes
Estadística y Probabilidad
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Open access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/15071