Repository: Freie Universität Berlin, Math Department

A large-deviations approach to gelation

Andreis, L. and König, W. and Patterson, R. I. A (2019) A large-deviations approach to gelation. SFB 1114 Preprint in arXiv:1901.01876 . pp. 1-22. (Unpublished)


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A large-deviations 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 time-dependent version of the Erdős-Rényi 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 Erdős-Rényi 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:29 Apr 2021 09:59

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