uu.seUppsala universitets publikationer
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Sharpness of the phase transition for continuum percolation in R2
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori. Inst Matematica Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
Univ Geneva, 2-4 Rue Lievre, CH-1211 Geneva, Switzerland.
Inst Matematica Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
2018 (Engelska)Ingår i: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 172, nr 1-2, s. 525-581Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the radii are uniformly bounded from above. In this article, we investigate this process for unbounded (and possibly heavy tailed) radii distributions. Under mild assumptions on the radius distribution, we show that both the vacant and occupied sets undergo a phase transition at the same critical parameter.c. Moreover, For. <.c, the vacant set has a unique unbounded connected component and we give precise bounds on the one-arm probability for the occupied set, depending on the radius distribution. At criticality, we establish the box-crossing property, implying that no unbounded component can be found, neither in the occupied nor the vacant sets. We provide a polynomial decay for the probability of the one-arm events, under sharp conditions on the distribution of the radius. For. >.c, the occupied set has a unique unbounded component and we prove that the one-arm probability for the vacant decays exponentially fast. The techniques we develop in this article can be applied to other models such as the Poisson Voronoi and confetti percolation.

Ort, förlag, år, upplaga, sidor
2018. Vol. 172, nr 1-2, s. 525-581
Nyckelord [en]
Percolation, Poisson point processes, Critical behavior, Sharp thresholds
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
URN: urn:nbn:se:uu:diva-366947DOI: 10.1007/s00440-017-0815-8ISI: 000443981900011OAI: oai:DiVA.org:uu-366947DiVA, id: diva2:1266571
Forskningsfinansiär
Vetenskapsrådet, 637-2013-7302Tillgänglig från: 2018-11-28 Skapad: 2018-11-28 Senast uppdaterad: 2018-11-28Bibliografiskt granskad

Open Access i DiVA

Fulltext saknas i DiVA

Övriga länkar

Förlagets fulltext

Personposter BETA

Ahlberg, Daniel

Sök vidare i DiVA

Av författaren/redaktören
Ahlberg, Daniel
Av organisationen
Analys och sannolikhetsteori
I samma tidskrift
Probability theory and related fields
Sannolikhetsteori och statistik

Sök vidare utanför DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetricpoäng

doi
urn-nbn
Totalt: 386 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf