A large-deviations approach to gelation
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2568 | |
dc.contributor.author | Andreis, Luisa | |
dc.contributor.author | König, Wolfgang | |
dc.contributor.author | Patterson, Robert | |
dc.date.accessioned | 2019-03-09T03:38:24Z | |
dc.date.available | 2019-06-28T08:10:33Z | |
dc.date.issued | 2019 | |
dc.description.abstract | 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 at time t = 1. Via a standard map of the multiplicative coalescent onto a time-dependent version of the Erdos-Rényi random graph, our results can also be rephrased as an LDP for the component sizes in that graph. Our proofs rely on estimates and asymptotics for the probability that smaller Erdos-Rényi graphs are connected. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/1835 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2745 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2568 | |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Coagulation process | eng |
dc.subject.other | multiplicative coalescent | eng |
dc.subject.other | gelation | eng |
dc.subject.other | phase transition | eng |
dc.subject.other | large deviations | eng |
dc.subject.other | Erd˝os-Rényi random graph | eng |
dc.title | A large-deviations approach to gelation | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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