The Equilibrium Behavior of Reversible Coagulation-Fragmentation Processes

Richard Durrett (), Boris L. Granovsky () and Shay Gueron ()
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Richard Durrett: Cornell University
Boris L. Granovsky: Israel Institute of Technology
Shay Gueron: Israel Institute of Technology

Journal of Theoretical Probability, 1999, vol. 12, issue 2, 447-474

Abstract: Abstract The coagulation-fragmentation process models the stochastic evolution of a population of N particles distributed into groups of different sizes that coagulate and fragment at given rates. The process arises in a variety of contexts and has been intensively studied for a long time. As a result, different approximations to the model were suggested. Our paper deals with the exact model which is viewed as a time-homogeneous interacting particle system on the state space Ω N, the set of all partitions of N. We obtain the stationary distribution (invariant measure) on Ω N for the whole class of reversible coagulation-fragmentation processes, and derive explicit expressions for important functionals of this measure, in particular, the expected numbers of groups of all sizes at the steady state. We also establish a characterization of the transition rates that guarantee the reversibility of the process. Finally, we make a comparative study of our exact solution and the approximation given by the steady-state solution of the coagulation-fragmentation integral equation, which is known in the literature. We show that in some cases the latter approximation can considerably deviate from the exact solution.

Keywords: Coagulation-fragmentation processes; interacting particle systems; reversibility; equilibrium (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1021682212351

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