On large deviation properties of Erdös-Rényi random graphs
نویسندگان
چکیده
It is well-known that typical properties of random graphs can be derived from the q → 1 limit of the Potts model of statistical mechanics. We show that, additionally, the Legendre transform of the Potts free energy with respect to ln q allows to study large deviation properties of the random graph ensemble characterizing graphs with an atypical number of components. We also demonstrate how the same results can be derived by studying the evolution of random graphs under the insertion of new vertices and edges, without recourse to the thermodynamics of the Potts model. PACS: 02.50.-r, 05.50.+q, 75.10.Nr
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تاریخ انتشار 2008