Exponential Approximation, Method of types for Empirical Neighbourhood Measures of Random graphs by Random Allocation
arXiv:1212.4281
Abstract
In this article we find exponential good approximation of the empirical neigbourhood distribution of symbolled random graphs conditioned to a given empirical symbol distribution and empirical pair distribution. Using this approximation we shorten or simplify the proof of (Doku-Amponsah and Morters 2010, Theorem~2.5); the large deviation principle (LDP) for empirical neigbourhood distribution of symbolled random graphs. We also show that the LDP for the empirical degree measure of the classical Erdős-Rényi graph is a special case of (Doku-Amponsah and Moerters, 2010, Theorem~2.5). From the LDP for the empirical degree measure, we derive an LDP for the the proportion of isolated vertices in the classical Erdős-Rényi graph.
11 pages