Andreis, L. and König, W. and Patterson, R. I. A (2019) A largedeviations approach to gelation. SFB 1114 Preprint in arXiv:1901.01876 . pp. 122. (Unpublished)

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Official URL: https://arxiv.org/abs/1901.01876
Abstract
A largedeviations principle (LDP) is derived for the state at fixed time, of the multiplicative coalescent in the large particle number limit. The rate function is explicit and describes each of the three parts of the state: microscopic, mesoscopic and macroscopic. In particular, it clearly captures the well known gelation phase transition given by the formation of a particle containing a positive fraction of the system mass. Via a standard map of the multiplicative coalescent onto a timedependent version of the ErdősRényi random graph, our results can also be rephrased as an LDP for the component sizes in that graph. The proofs rely on estimates and asymptotics for the probability that smaller ErdősRényi graphs are connected.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  2285 
Deposited By:  Silvia Hoemke 
Deposited On:  08 Jan 2019 16:21 
Last Modified:  08 Jan 2019 16:21 
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