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May 2013 Gelation for Marcus–Lushnikov process
Fraydoun Rezakhanlou
Ann. Probab. 41(3B): 1806-1830 (May 2013). DOI: 10.1214/11-AOP691


The Marcus–Lushnikov process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get large, giant particles emerge in finite time. This is known as gelation, and such particles are known as gels. Gelation comes in different flavors: simple, instantaneous and complete. In the case of an instantaneous gelation, giant particles are formed in a very short time. If all particles coagulate to form a single particle in a time interval that stays bounded as total mass gets large, then we have a complete gelation. In this article, we describe conditions which guarantee any of the three possible gelations with explicit bounds on the size of gels and the time of their creations.


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Fraydoun Rezakhanlou. "Gelation for Marcus–Lushnikov process." Ann. Probab. 41 (3B) 1806 - 1830, May 2013.


Published: May 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1278.82074
MathSciNet: MR3098059
Digital Object Identifier: 10.1214/11-AOP691

Primary: 74A25
Secondary: 60K35

Keywords: coagulation , gelation , Marcus–Lushnikov process

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 3B • May 2013
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