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Asymptotics of counts of small components in random structures and models of coagulation-fragmentation

Boris L. Granovsky (2013)

ESAIM: Probability and Statistics

We establish necessary and sufficient conditions for the convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. The multiplicative measures depict distributions of component spectra of random structures and also the equilibria of classic models of statistical mechanics and stochastic processes of coagulation-fragmentation. We show that the convergence of multiplicative measures is equivalent to the asymptotic independence of counts of...

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