Coagulation processes with Gibbsian time evolution
Autor: | Granovsky, Boris, Kryvoshaev, Alexander |
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Rok vydání: | 2010 |
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Druh dokumentu: | Working Paper |
Popis: | 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 $t>0.$ Comment: 22 pages. Changes made implementing referee's suggestions and remarks.This is a final version to be published in the Advances of Applied probability |
Databáze: | arXiv |
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