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dc.contributor.author
Erhard, Dirk
dc.contributor.author
Martínez Linares, Julián Facundo
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dc.contributor.author
Poisat, Julien
dc.date.available
2017-06-26T18:16:41Z
dc.date.issued
2016-01
dc.identifier.citation
Erhard, Dirk; Martínez Linares, Julián Facundo; Poisat, Julien; Brownian Paths Homogeneously Distributed in Space: Percolation Phase Transition and Uniqueness of the Unbounded Cluster; Springer; Journal Of Theoretical Probability; 1-2016; 1-29
dc.identifier.issn
0894-9840
dc.identifier.uri
http://hdl.handle.net/11336/18886
dc.description.abstract
We consider a continuum percolation model on Rd , d ≥ 1. For t, λ ∈ (0,∞) and d ∈ {1, 2, 3}, the occupied set is given by the union of independent Brownian paths running up to time t whose initial points form a Poisson point process with intensity λ > 0. When d ≥ 4, the Brownian paths are replaced by Wiener sausages with radius r > 0. We establish that, for d = 1 and all choices of t, no percolation occurs, whereas for d ≥ 2, there is a non-trivial percolation transition in t, provided λ and r are chosen properly. The last statement means that λ has to be chosen to be strictly smaller than the critical percolation parameter for the occupied set at time zero (which is infinite when d ∈ {2, 3}, but finite and dependent on r when d ≥ 4). We further show that for all d ≥ 2, the unbounded cluster in the supercritical phase is unique. Along the way a finite box criterion for non-percolation in the Boolean model is extended to radius distributions with an exponential tail. This may be of independent interest. The present paper settles the basic properties of the model and should be viewed as a springboard for finer results.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Continuum Percolation
dc.subject
Brownian Motion
dc.subject.classification
Estadística y Probabilidad
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Brownian Paths Homogeneously Distributed in Space: Percolation Phase Transition and Uniqueness of the Unbounded Cluster
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-06-26T14:09:12Z
dc.identifier.eissn
1572-9230
dc.journal.pagination
1-29
dc.journal.pais
Estados Unidos
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dc.description.fil
Fil: Erhard, Dirk. University Of Warwick; Reino Unido
dc.description.fil
Fil: Martínez Linares, Julián Facundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.description.fil
Fil: Poisat, Julien. Université Paris-Dauphine; Francia
dc.journal.title
Journal Of Theoretical Probability
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s10959-015-0661-5
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10959-015-0661-5
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1311.2907
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