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Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

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Abstract

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of the equilibrium measure for a wide class of parameter functions of the process. This formula proves the conjecture stated in [5] for the above class of processes. The method used goes back to A. Khintchine.

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Authors and Affiliations

  1. School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Gregory A. Freiman

  2. Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Boris L. Granovsky

Authors
  1. Gregory A. Freiman
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  2. Boris L. Granovsky
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Correspondence to Gregory A. Freiman.

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Freiman, G.A., Granovsky, B.L. Asymptotic formula for a partition function of reversible coagulation-fragmentation processes. Isr. J. Math. 130, 259–279 (2002). https://doi.org/10.1007/BF02764079

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  • DOI: https://doi.org/10.1007/BF02764079

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