Scale-Free Percolation in Continuum Space
The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice Z d , d ≥ 1 , because it fulfills several stylized facts observed in large real-life networks. We adopt this model to continuum space which leads to...
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| Veröffentlicht in: | Communications in mathematics and statistics 2019-09, Vol.7 (3), p.269-308 |
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| creator | Deprez, Philippe Wüthrich, Mario V. |
| description | The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice
Z
d
,
d
≥
1
, because it fulfills several stylized facts observed in large real-life networks. We adopt this model to continuum space which leads to a heterogeneous random-connection model on
R
d
: Particles are generated by a homogeneous marked Poisson point process on
R
d
, and the probability of an edge between two particles is determined by their marks and their distance. In this model we study several properties such as the degree distributions, percolation properties and graph distances. |
| doi_str_mv | 10.1007/s40304-018-0142-0 |
| format | Article |
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Z
d
,
d
≥
1
, because it fulfills several stylized facts observed in large real-life networks. We adopt this model to continuum space which leads to a heterogeneous random-connection model on
R
d
: Particles are generated by a homogeneous marked Poisson point process on
R
d
, and the probability of an edge between two particles is determined by their marks and their distance. In this model we study several properties such as the degree distributions, percolation properties and graph distances.</description><identifier>ISSN: 2194-6701</identifier><identifier>EISSN: 2194-671X</identifier><identifier>DOI: 10.1007/s40304-018-0142-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Mathematics ; Mathematics and Statistics ; Percolation ; Statistics</subject><ispartof>Communications in mathematics and statistics, 2019-09, Vol.7 (3), p.269-308</ispartof><rights>School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-bdd8c18dd885e95a609823c80b2f6e8ae0b138baa3f0a4b44ffd49f8a0e76fa63</citedby><cites>FETCH-LOGICAL-c316t-bdd8c18dd885e95a609823c80b2f6e8ae0b138baa3f0a4b44ffd49f8a0e76fa63</cites><orcidid>0000-0003-0813-0603</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40304-018-0142-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40304-018-0142-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27907,27908,41471,42540,51302</link.rule.ids></links><search><creatorcontrib>Deprez, Philippe</creatorcontrib><creatorcontrib>Wüthrich, Mario V.</creatorcontrib><title>Scale-Free Percolation in Continuum Space</title><title>Communications in mathematics and statistics</title><addtitle>Commun. Math. Stat</addtitle><description>The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice
Z
d
,
d
≥
1
, because it fulfills several stylized facts observed in large real-life networks. We adopt this model to continuum space which leads to a heterogeneous random-connection model on
R
d
: Particles are generated by a homogeneous marked Poisson point process on
R
d
, and the probability of an edge between two particles is determined by their marks and their distance. In this model we study several properties such as the degree distributions, percolation properties and graph distances.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Percolation</subject><subject>Statistics</subject><issn>2194-6701</issn><issn>2194-671X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kMtKxDAUhoMoOIzzAO4KrlxETy5N06UUR4UBhVFwF9L0RDp02pq0C9_eloquXJzL4r_AR8glgxsGkN1GCQIkBaankZzCCVlxlkuqMvZ--vsDOyebGA8AwBTXWZ6uyPXe2QbpNiAmLxhc19ih7tqkbpOia4e6Hcdjsu-twwty5m0TcfNz1-Rte_9aPNLd88NTcbejTjA10LKqtGN62jrFPLUKcs2F01Byr1BbhJIJXVorPFhZSul9JXOvLWCmvFViTa6W3D50nyPGwRy6MbRTpeFcKQkgUphUbFG50MUY0Js-1EcbvgwDM0MxCxQzQTEzFDN7-OKJk7b9wPCX_L_pG5l9Ys4</recordid><startdate>20190901</startdate><enddate>20190901</enddate><creator>Deprez, Philippe</creator><creator>Wüthrich, Mario V.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-0813-0603</orcidid></search><sort><creationdate>20190901</creationdate><title>Scale-Free Percolation in Continuum Space</title><author>Deprez, Philippe ; Wüthrich, Mario V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-bdd8c18dd885e95a609823c80b2f6e8ae0b138baa3f0a4b44ffd49f8a0e76fa63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Percolation</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Deprez, Philippe</creatorcontrib><creatorcontrib>Wüthrich, Mario V.</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematics and statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Deprez, Philippe</au><au>Wüthrich, Mario V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Scale-Free Percolation in Continuum Space</atitle><jtitle>Communications in mathematics and statistics</jtitle><stitle>Commun. Math. Stat</stitle><date>2019-09-01</date><risdate>2019</risdate><volume>7</volume><issue>3</issue><spage>269</spage><epage>308</epage><pages>269-308</pages><issn>2194-6701</issn><eissn>2194-671X</eissn><abstract>The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice
Z
d
,
d
≥
1
, because it fulfills several stylized facts observed in large real-life networks. We adopt this model to continuum space which leads to a heterogeneous random-connection model on
R
d
: Particles are generated by a homogeneous marked Poisson point process on
R
d
, and the probability of an edge between two particles is determined by their marks and their distance. In this model we study several properties such as the degree distributions, percolation properties and graph distances.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40304-018-0142-0</doi><tpages>40</tpages><orcidid>https://orcid.org/0000-0003-0813-0603</orcidid></addata></record> |
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| language | eng |
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| subjects | Mathematics Mathematics and Statistics Percolation Statistics |
| title | Scale-Free Percolation in Continuum Space |
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