Reversible coagulation-fragmentation processes and random combinatorial structures: asymptotics for the number of groups

Authors:
Michael M. Erlihson;Boris L. Granovsky
Affiliations:
Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel;Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel
Venue:
Random Structures & Algorithms
Year:
2004

Citing 3
Cited 2

Systems in stochastic equilibrium

Systems in stochastic equilibrium
Enumerative combinatorics

Enumerative combinatorics
Random graphs

Random graphs

Two-parameter poisson–dirichlet measures and reversible exchangeable fragmentation–coalescence processes

Combinatorics, Probability and Computing
Ergodicity of multiplicative statistics

Journal of Combinatorial Theory Series A

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Abstract

The equilibrium distribution of a reversible coagulation-fragmentation process (CFP) and the joint distribution of components of a random combinatorial structure (RCS) are given by the same probability measure on the set of partitions. We establish a central limit theorem for the number of groups (= components) in the case a(k) = qkp-1, k ≥ 1, q, p 0, where a(k), k ≥ 1, is the parameter function that induces the invariant measure. The result obtained is compared with the ones for logarithmic RCS's and for RCS's, corresponding to the case p