Limiting shape for first-passage percolation models on random geometric graphs
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2877 | |
dc.contributor.author | Coletti, Cristian F. | |
dc.contributor.author | de Lima, Lucas R. | |
dc.contributor.author | Hinsen, Alexander | |
dc.contributor.author | Jahnel, Benedikt | |
dc.contributor.author | Valesin, Daniel R. | |
dc.date.accessioned | 2022-07-05T14:28:47Z | |
dc.date.available | 2022-07-05T14:28:47Z | |
dc.date.issued | 2021 | |
dc.description.abstract | Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed random variables on the random infinite connected component. We provide sufficient conditions for the existence of the asymptotic shape and we show that the shape is an Euclidean ball. We give some examples exhibiting the result for Bernoulli percolation and the Richardson model. For the Richardson model we further show that it converges weakly to a branching process in the joint limit of large intensities and slow passing times. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9595 | |
dc.identifier.uri | https://doi.org/10.34657/8633 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2877 | |
dc.relation.issn | 2198-5855 | |
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 | |
dc.subject.other | Poisson--Gilbert graph | eng |
dc.subject.other | Richardson model | eng |
dc.subject.other | Bernoulli bond percolation | eng |
dc.subject.other | subergodicity | eng |
dc.subject.other | high-density limit | eng |
dc.subject.other | isotropic shapes | eng |
dc.title | Limiting shape for first-passage percolation models on random geometric graphs | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 19 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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