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September 2012 Coagulation processes with Gibbsian time evolution
Boris L. Granovsky, Alexander V. Kryvoshaev
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J. Appl. Probab. 49(3): 612-626 (September 2012). DOI: 10.1239/jap/1346955321

Abstract

We prove that a stochastic process of pure coagulation has at any timet ≥ 0 a time-dependent Gibbs distribution if and only if therates ψ(i, j) of single coagulations are of the formψ(i; j) = if(j) + jf(i), wheref is an arbitrary nonnegative function on the set of positive integers.We also obtain a recurrence relation for weights of these Gibbs distributionsthat allow us to derive the general form of the solution and the explicitsolutions in three particular cases of the function f. For the threecorresponding models, we study the probability of coagulation into one giantcluster by time t > 0.

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Boris L. Granovsky. Alexander V. Kryvoshaev. "Coagulation processes with Gibbsian time evolution." J. Appl. Probab. 49 (3) 612 - 626, September 2012. https://doi.org/10.1239/jap/1346955321

Information

Published: September 2012
First available in Project Euclid: 6 September 2012

zbMATH: 1252.82070
MathSciNet: MR3012087
Digital Object Identifier: 10.1239/jap/1346955321

Subjects:
Primary: 82C23
Secondary: 05A18, 60J27

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 3 • September 2012
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