Math @ Duke

Publications [#243479] of Richard T. Durrett
Papers Published
 Durrett, R; Granovsky, BL; Gueron, S, The Equilibrium Behavior of Reversible CoagulationFragmentation Processes,
Journal of Theoretical Probability, vol. 12 no. 2
(1999),
pp. 447474
(last updated on 2017/12/16)
Abstract: The coagulationfragmentation 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 timehomogeneous interacting particle system on the state space ΩN, the set of all partitions of N. We obtain the stationary distribution (invariant measure) on ΩN for the whole class of reversible coagulationfragmentation 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 steadystate solution of the coagulationfragmentation integral equation, which is known in the literature. We show that in some cases the latter approximation can considerably deviate from the exact solution.


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