Coagulation processes with Gibbsian time evolution

Details Coagulation processes with Gibbsian time evolution Coagulation processes with Gibbsian time evolution

2010-08-05

arxiv.org/abs/1008.1027v2

Mathematics

Probability

22 pages. Changes made implementing referee's suggestions and remarks.This is a final version to be published in the Advances

Scientific paper

We prove that time dynamics of a stochastic process of pure coagulation is given by a time dependent Gibbs distribution if and only if rates of single coagulations have the form $\psi(i,j)=if(j)+jf(i)$, where $f$ is an arbitrary nonnegative function on the set of integers $\ge 1$. We also obtained a recurrence relation for weights of these Gibbs distributions, that allowed explicit solutions in three particular cases of the function $f$. For the three corresponding models, we study the probability of coagulation into one giant cluster, at time $t>0.$

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