1,527 research outputs found
Joint large deviation result for empirical measures of the coloured random geometric graphs
We prove joint large deviation principle for the \emph{ empirical pair
measure} and \emph{empirical locality measure} of the \emph{near intermediate}
coloured random geometric graph models on points picked uniformly in a
dimensional torus of a unit circumference.From this result we obtain large
deviation principles for the \emph{number of edges per vertex}, the
\emph{degree distribution and the proportion of isolated vertices } for the
\emph{near intermediate} random geometric graph models.Comment: 13 pages. arXiv admin note: substantial text overlap with
arXiv:1312.632
Asymptotics of the partition function of Ising model on inhomogeneous random graphs
For a finite random graph, we defined a simple model of statistical
mechanics. We obtain an annealed asymptotic result for the random partition
function for this model on finite random graphs as n; the size of the graph is
very large. To obtain this result, we define the empirical bond distribution,
which enumerates the number of bonds between a given couple of spins, and
empirical spin distribution, which enumerates the number of sites having a
given spin on the spinned random graphs. For these empirical distributions we
extend the large deviation principle(LDP) to cover random graphs with
continuous colour laws. Applying Varandhan Lemma and this LDP to the
Hamiltonian of the Ising model defined on Erdos-Renyi graphs, expressed as a
function of the empirical distributions, we obtain our annealed asymptotic
result.Comment: 14 page
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