FINITARY COLORING
Suppose that the vertices of ℤd are assigned random colors via a finitary factor of independent identically distributed (i.i.d.) vertex-labels. That is, the color of vertex v is determined by a rule that examines the labels within a finite (but random and perhaps unbounded) distance R of v, and the...
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| Veröffentlicht in: | The Annals of probability 2017-09, Vol.45 (5), p.2867-2898 |
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| container_title | The Annals of probability |
| container_volume | 45 |
| creator | Holroyd, Alexander E. Schramm, Oded Wilson, David B. |
| description | Suppose that the vertices of ℤd are assigned random colors via
a finitary factor of independent identically distributed (i.i.d.)
vertex-labels. That is, the color of vertex v is determined by a rule
that examines the labels within a finite (but random and perhaps
unbounded) distance R of v, and the same rule applies at all vertices.
We investigate the tail behavior of R if the coloring is required to be
proper (i.e., if adjacent vertices must receive different colors). When
d ≥ 2, the optimal tail is given by a power law for 3 colors, and a
tower (iterated exponential) function for 4 or more colors (and also for
3 or more colors when d = 1). If proper coloring is replaced with any
shift of finite type in dimension 1, then, apart from trivial cases,
tower function behavior also applies. |
| doi_str_mv | 10.1214/16-AOP1127 |
| format | Article |
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a finitary factor of independent identically distributed (i.i.d.)
vertex-labels. That is, the color of vertex v is determined by a rule
that examines the labels within a finite (but random and perhaps
unbounded) distance R of v, and the same rule applies at all vertices.
We investigate the tail behavior of R if the coloring is required to be
proper (i.e., if adjacent vertices must receive different colors). When
d ≥ 2, the optimal tail is given by a power law for 3 colors, and a
tower (iterated exponential) function for 4 or more colors (and also for
3 or more colors when d = 1). If proper coloring is replaced with any
shift of finite type in dimension 1, then, apart from trivial cases,
tower function behavior also applies.</description><identifier>ISSN: 0091-1798</identifier><identifier>EISSN: 2168-894X</identifier><identifier>DOI: 10.1214/16-AOP1127</identifier><language>eng</language><publisher>Hayward: Institute of Mathematical Statistics</publisher><subject>Coloring ; Graph coloring ; Labels ; Studies</subject><ispartof>The Annals of probability, 2017-09, Vol.45 (5), p.2867-2898</ispartof><rights>Copyright © 2017 Institute of Mathematical Statistics</rights><rights>Copyright Institute of Mathematical Statistics Sep 2017</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-98ddb70ae2ccd324bb7457abc7f89773512906a6cd5bb4d054a7cffffd9aa7893</citedby><cites>FETCH-LOGICAL-c325t-98ddb70ae2ccd324bb7457abc7f89773512906a6cd5bb4d054a7cffffd9aa7893</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/26362520$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/26362520$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Holroyd, Alexander E.</creatorcontrib><creatorcontrib>Schramm, Oded</creatorcontrib><creatorcontrib>Wilson, David B.</creatorcontrib><title>FINITARY COLORING</title><title>The Annals of probability</title><description>Suppose that the vertices of ℤd are assigned random colors via
a finitary factor of independent identically distributed (i.i.d.)
vertex-labels. That is, the color of vertex v is determined by a rule
that examines the labels within a finite (but random and perhaps
unbounded) distance R of v, and the same rule applies at all vertices.
We investigate the tail behavior of R if the coloring is required to be
proper (i.e., if adjacent vertices must receive different colors). When
d ≥ 2, the optimal tail is given by a power law for 3 colors, and a
tower (iterated exponential) function for 4 or more colors (and also for
3 or more colors when d = 1). If proper coloring is replaced with any
shift of finite type in dimension 1, then, apart from trivial cases,
tower function behavior also applies.</description><subject>Coloring</subject><subject>Graph coloring</subject><subject>Labels</subject><subject>Studies</subject><issn>0091-1798</issn><issn>2168-894X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNpNz81KxDAUBeAgCtbRhT6BIG6EaG7-brMsxRkLZSrDCLoKadqCRe2YdBa-vZXOwru5m49zOIRcAbsHDvIBNM2qZwCORyThoFOaGvl6TBLGDFBAk56Ssxh7xphGlAm5XBbrYptt3q7zqqw2xXp1Tk469xHbi8NfkJfl4zZ_omW1KvKspF5wNVKTNk2NzLXc-0ZwWdcoFbraY5caRKGAG6ad9o2qa9kwJR36brrGOIepEQtyM-fuwvC9b-No-2EfvqZKC0aDnFqUnNTdrHwYYgxtZ3fh_dOFHwvM_k22oO1h8oRvZ9zHcQj_JRcMLddCc8WZ-AVxZ1DT</recordid><startdate>20170901</startdate><enddate>20170901</enddate><creator>Holroyd, Alexander E.</creator><creator>Schramm, Oded</creator><creator>Wilson, David B.</creator><general>Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20170901</creationdate><title>FINITARY COLORING</title><author>Holroyd, Alexander E. ; Schramm, Oded ; Wilson, David B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-98ddb70ae2ccd324bb7457abc7f89773512906a6cd5bb4d054a7cffffd9aa7893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Coloring</topic><topic>Graph coloring</topic><topic>Labels</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Holroyd, Alexander E.</creatorcontrib><creatorcontrib>Schramm, Oded</creatorcontrib><creatorcontrib>Wilson, David B.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The Annals of probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Holroyd, Alexander E.</au><au>Schramm, Oded</au><au>Wilson, David B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>FINITARY COLORING</atitle><jtitle>The Annals of probability</jtitle><date>2017-09-01</date><risdate>2017</risdate><volume>45</volume><issue>5</issue><spage>2867</spage><epage>2898</epage><pages>2867-2898</pages><issn>0091-1798</issn><eissn>2168-894X</eissn><abstract>Suppose that the vertices of ℤd are assigned random colors via
a finitary factor of independent identically distributed (i.i.d.)
vertex-labels. That is, the color of vertex v is determined by a rule
that examines the labels within a finite (but random and perhaps
unbounded) distance R of v, and the same rule applies at all vertices.
We investigate the tail behavior of R if the coloring is required to be
proper (i.e., if adjacent vertices must receive different colors). When
d ≥ 2, the optimal tail is given by a power law for 3 colors, and a
tower (iterated exponential) function for 4 or more colors (and also for
3 or more colors when d = 1). If proper coloring is replaced with any
shift of finite type in dimension 1, then, apart from trivial cases,
tower function behavior also applies.</abstract><cop>Hayward</cop><pub>Institute of Mathematical Statistics</pub><doi>10.1214/16-AOP1127</doi><tpages>32</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0091-1798 |
| ispartof | The Annals of probability, 2017-09, Vol.45 (5), p.2867-2898 |
| issn | 0091-1798 2168-894X |
| language | eng |
| recordid | cdi_proquest_journals_1961432554 |
| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | Coloring Graph coloring Labels Studies |
| title | FINITARY COLORING |
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