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

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 531-549
- ISSN: 1292-8100

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topGranovsky, Boris L.. "Asymptotics of counts of small components in random structures and models of coagulation-fragmentation." ESAIM: Probability and Statistics 17 (2013): 531-549. <http://eudml.org/doc/273628>.

@article{Granovsky2013,

abstract = {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 components of fixed sizes in random structures. We then apply Schur’s tauberian lemma and some results from additive number theory and enumerative combinatorics in order to derive plausible sufficient conditions of convergence. Our results demonstrate that the common belief, that counts of components of fixed sizes in random structures become independent as the number of particles goes to infinity, is not true in general.},

author = {Granovsky, Boris L.},

journal = {ESAIM: Probability and Statistics},

keywords = {multiplicative measures on the set of partitions; random structures; coagulation-fragmentation processes; Schur’s lemma; models of ideal gas; random combinatorial structures; conditioning relation; Schur lemma; asymptotic independence; ideal gas models},

language = {eng},

pages = {531-549},

publisher = {EDP-Sciences},

title = {Asymptotics of counts of small components in random structures and models of coagulation-fragmentation},

url = {http://eudml.org/doc/273628},

volume = {17},

year = {2013},

}

TY - JOUR

AU - Granovsky, Boris L.

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

JO - ESAIM: Probability and Statistics

PY - 2013

PB - EDP-Sciences

VL - 17

SP - 531

EP - 549

AB - 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 components of fixed sizes in random structures. We then apply Schur’s tauberian lemma and some results from additive number theory and enumerative combinatorics in order to derive plausible sufficient conditions of convergence. Our results demonstrate that the common belief, that counts of components of fixed sizes in random structures become independent as the number of particles goes to infinity, is not true in general.

LA - eng

KW - multiplicative measures on the set of partitions; random structures; coagulation-fragmentation processes; Schur’s lemma; models of ideal gas; random combinatorial structures; conditioning relation; Schur lemma; asymptotic independence; ideal gas models

UR - http://eudml.org/doc/273628

ER -

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