The coagulation-fragmentation hierarchy with homogeneous rates and underlying stochastic dynamics

2018/08/31 by Kenji Handa, Handa, Kenji
Economics, Econometrics and Finance · Mathematics · #60K35 #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1808.10674

openalex publication_date 2018/08/31 · openalex created_date 2018/09/07 · openalex updated_date 2026/07/28

Abstract

A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by correlation measures for stochastic dynamics of interval partitions evolving according to some split-merge transformations. Regarding those processes, a sufficient condition for a distribution to be reversible is given. Also, an asymptotic result for properly rescaled processes is shown to obtain a solution to a nonlinear equation called the coagulation-fragmentation equation.

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