Local Convergence of Random Graph Colorings
Let G = G ( n , m ) be a random graph whose average degree d = 2 m / n is below the k -colorability threshold. If we sample a k -coloring σ of G uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from stat...
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| Veröffentlicht in: | Combinatorica (Budapest. 1981) 2018-04, Vol.38 (2), p.341-380 |
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| container_title | Combinatorica (Budapest. 1981) |
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| creator | Coja-Oghlan, Amin Efthymiou, Charilaos Jaafari, Nor |
| description | Let
G
=
G
(
n
,
m
) be a random graph whose average degree
d
= 2
m
/
n
is below the
k
-colorability threshold. If we sample a
k
-coloring
σ
of
G
uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called
condensation threshold d
k
,cond
, the colors assigned to far away vertices are asymptotically independent [Krzakala et al.: Proc. National Academy of Sciences 2007]. We prove this conjecture for
k
exceeding a certain constant
k
0
. More generally, we investigate the joint distribution of the
k
-colorings that
σ
induces locally on the bounded-depth neighborhoods of any fixed number of vertices. In addition, we point out an implication on the
reconstruction problem. |
| doi_str_mv | 10.1007/s00493-016-3394-x |
| format | Article |
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G
=
G
(
n
,
m
) be a random graph whose average degree
d
= 2
m
/
n
is below the
k
-colorability threshold. If we sample a
k
-coloring
σ
of
G
uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called
condensation threshold d
k
,cond
, the colors assigned to far away vertices are asymptotically independent [Krzakala et al.: Proc. National Academy of Sciences 2007]. We prove this conjecture for
k
exceeding a certain constant
k
0
. More generally, we investigate the joint distribution of the
k
-colorings that
σ
induces locally on the bounded-depth neighborhoods of any fixed number of vertices. In addition, we point out an implication on the
reconstruction problem.</description><identifier>ISSN: 0209-9683</identifier><identifier>EISSN: 1439-6912</identifier><identifier>DOI: 10.1007/s00493-016-3394-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Combinatorics ; Graph coloring ; Mathematics ; Mathematics and Statistics ; Original Paper</subject><ispartof>Combinatorica (Budapest. 1981), 2018-04, Vol.38 (2), p.341-380</ispartof><rights>János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2017</rights><rights>COPYRIGHT 2018 Springer</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c398t-4cce7ac5e91d92a4064346c3f22c69cffdc8a84a4a892dc6ca94057bf1d9fe413</citedby><cites>FETCH-LOGICAL-c398t-4cce7ac5e91d92a4064346c3f22c69cffdc8a84a4a892dc6ca94057bf1d9fe413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00493-016-3394-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00493-016-3394-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Coja-Oghlan, Amin</creatorcontrib><creatorcontrib>Efthymiou, Charilaos</creatorcontrib><creatorcontrib>Jaafari, Nor</creatorcontrib><title>Local Convergence of Random Graph Colorings</title><title>Combinatorica (Budapest. 1981)</title><addtitle>Combinatorica</addtitle><description>Let
G
=
G
(
n
,
m
) be a random graph whose average degree
d
= 2
m
/
n
is below the
k
-colorability threshold. If we sample a
k
-coloring
σ
of
G
uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called
condensation threshold d
k
,cond
, the colors assigned to far away vertices are asymptotically independent [Krzakala et al.: Proc. National Academy of Sciences 2007]. We prove this conjecture for
k
exceeding a certain constant
k
0
. More generally, we investigate the joint distribution of the
k
-colorings that
σ
induces locally on the bounded-depth neighborhoods of any fixed number of vertices. In addition, we point out an implication on the
reconstruction problem.</description><subject>Combinatorics</subject><subject>Graph coloring</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><issn>0209-9683</issn><issn>1439-6912</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KAzEURoMoWKsP4G7ApaTe_DQzWZaiVSgIousQ7yR1ynQyJlOpb2_KCK7kLgI338kXDiHXDGYMoLxLAFILCkxRIbSkhxMyYVJoqjTjp2QCHDTVqhLn5CKlLQBUgs0n5HYd0LbFMnRfLm5ch64IvnixXR12xSra_iPftSE23SZdkjNv2-Sufs8peXu4f10-0vXz6mm5WFMUuhqoRHSlxbnTrNbcSlBSSIXCc45Ko_c1VraSVtpK8xoVWi1hXr77HPdOMjElN-O7fQyfe5cGsw372OVKw0FUIECVMqdmY2pjW2eazochWsxTu12DoXO-yftFyTWDXFRmgI0AxpBSdN70sdnZ-G0YmKNEM0o0WaI5SjSHzPCRSf1RgYt_X_kf-gEJVXN-</recordid><startdate>20180401</startdate><enddate>20180401</enddate><creator>Coja-Oghlan, Amin</creator><creator>Efthymiou, Charilaos</creator><creator>Jaafari, Nor</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180401</creationdate><title>Local Convergence of Random Graph Colorings</title><author>Coja-Oghlan, Amin ; Efthymiou, Charilaos ; Jaafari, Nor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c398t-4cce7ac5e91d92a4064346c3f22c69cffdc8a84a4a892dc6ca94057bf1d9fe413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Combinatorics</topic><topic>Graph coloring</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Coja-Oghlan, Amin</creatorcontrib><creatorcontrib>Efthymiou, Charilaos</creatorcontrib><creatorcontrib>Jaafari, Nor</creatorcontrib><collection>CrossRef</collection><jtitle>Combinatorica (Budapest. 1981)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Coja-Oghlan, Amin</au><au>Efthymiou, Charilaos</au><au>Jaafari, Nor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Local Convergence of Random Graph Colorings</atitle><jtitle>Combinatorica (Budapest. 1981)</jtitle><stitle>Combinatorica</stitle><date>2018-04-01</date><risdate>2018</risdate><volume>38</volume><issue>2</issue><spage>341</spage><epage>380</epage><pages>341-380</pages><issn>0209-9683</issn><eissn>1439-6912</eissn><abstract>Let
G
=
G
(
n
,
m
) be a random graph whose average degree
d
= 2
m
/
n
is below the
k
-colorability threshold. If we sample a
k
-coloring
σ
of
G
uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called
condensation threshold d
k
,cond
, the colors assigned to far away vertices are asymptotically independent [Krzakala et al.: Proc. National Academy of Sciences 2007]. We prove this conjecture for
k
exceeding a certain constant
k
0
. More generally, we investigate the joint distribution of the
k
-colorings that
σ
induces locally on the bounded-depth neighborhoods of any fixed number of vertices. In addition, we point out an implication on the
reconstruction problem.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00493-016-3394-x</doi><tpages>40</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0209-9683 |
| ispartof | Combinatorica (Budapest. 1981), 2018-04, Vol.38 (2), p.341-380 |
| issn | 0209-9683 1439-6912 |
| language | eng |
| recordid | cdi_proquest_journals_2038030674 |
| source | Springer Online Journals Complete |
| subjects | Combinatorics Graph coloring Mathematics Mathematics and Statistics Original Paper |
| title | Local Convergence of Random Graph Colorings |
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