Change search

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
On the easiest way to connect k points in the Random Interlacements process
Univ Paris 09, CEREMADE, UMR CNRS 7534, F-75775 Paris 16, France..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Latin American Journal of Probability and Mathematical Statistics, ISSN 1980-0436, E-ISSN 1980-0436, Vol. 10, no 1, p. 505-524Article in journal (Refereed) Published
##### Abstract [en]

We consider the random interlacements process with intensity u on Z(d), d >= 5 (call it I-u), built from a Poisson point process on the space of doubly infinite nearest neighbor trajectories on Z(d). For k >= 3 we want to determine the minimal number of trajectories from the point process that is needed to link together k points in I-u. Let n(k, d) := [d/2(k -1)] - (k - 2). We prove that almost surely given any k points x(1),..., x(k) is an element of I-u, there is a sequence of n(k, d) trajectories gamma(1),..., gamma(n(k,d)) from the underlying Poisson point process such that the union of their traces U-i =1(n(k,d)) Tr(gamma(i)) is a connected set containing x(1),..., x(k). Moreover we show that this result is sharp, i.e. that a.s. one can find x(1),..., x(k) is an element of I-u that cannot be linked together by n(k, d) - 1 trajectories.

##### Place, publisher, year, edition, pages
2013. Vol. 10, no 1, p. 505-524
##### Keywords [en]
Random Interlacement, Connectivity, Percolation, Random Walk
##### National Category
Algebra and Logic
##### Identifiers
ISI: 000346350100020OAI: oai:DiVA.org:uu-309907DiVA, id: diva2:1056710
Available from: 2016-12-15 Created: 2016-12-08 Last updated: 2017-11-29Bibliographically approved

#### Open Access in DiVA

##### File information
File name FULLTEXT01.pdfFile size 320 kBChecksum SHA-512
b4cb96702547966b1bcdd07045d07622d1c80242c445c8c84f67de366810a61905ffeda05ee2ed19c2361c61a7f912378cba0c2bf6a2e0c1c2d05f3c7983fb78
Type fulltextMimetype application/pdf

##### By organisation
Department of Mathematics
##### In the same journal
Latin American Journal of Probability and Mathematical Statistics
##### On the subject
Algebra and Logic

#### Search outside of DiVA

The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available
urn-nbn

#### Altmetric score

urn-nbn
Total: 325 hits

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
v. 2.35.3
|