Год выпуска: 2012 Автор: Kwabena Doku-Amponsah Издательство: LAP Lambert Academic Publishing Страниц: 184 ISBN: 9783659260346
Описание
For suitably defined empirical measures of a class of models of sparse coloured random graphs, we prove large deviation principles,with rate functions explicitly expressed in terms of relative entropies, in the weak topology. Also, under fairly general assumption we prove a joint large deviation principle (LDP), for the empirical pair measure and empirical offspring measure of multitype Galton-Watson tree conditioned to have exactly n vertices in the weak topology. Using these large deviation principles, we find asymptotic equipartition properties for hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as coloured random graphs). From our LDP results, we compute Thermodynamic limit of physical quantities such as the magnetization, specific heat, internal energy, susceptibility for the ferromagnetic Ising model on a finite random network.
