Gibbs random graphs on point processes

Consider a discrete locally finite subset Gamma of R(d) and the cornplete graph (Gamma, E), with vertices Gamma and edges E. We consider Gibbs measures on the set of sub-graphs with vertices Gamma and edges E` subset of 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 Gamma is sampled from a homogeneous Poisson process; and (b) for a fixed Gamma with sufficiently sparse points. (c) 2010 American Institute of Physics. [doi:10.1063/1.3514605]

CNPq[300576/92-7]

CNPq[662177/96-7]

CNPq[471891/2006-1]

CNPq[309397/2008-1]

CNPq[471946/2008-7]

CNPq[306092/2007-7]

PRONEX[99/11962-9]

RFBR[07-01-92216]

RFBR[08-01-00105]

(FAPERJ) Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro[E-26/170.008/2008]

(FAPERJ) Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro[E-26/110.982/2008]

(FAPERJ) Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro[E26/170.008/2008]