Exponential Approximation, Method of Types for Empirical Neighbourhood Distributions of Random Graphs by Random Allocations

K. Doku-Amponsah


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 \& 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 Erd\H{o}s-R\'{e}nyi graph is a special case of (Doku-Amponsah \& 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 Erd\H{o}s-R\'{e}nyi graph.

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DOI: http://dx.doi.org/10.5539/ijsp.v3n2p110


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International Journal of Statistics and Probability   ISSN 1927-7032(Print)   ISSN 1927-7040(Online)

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