Translation Invariant Extensions of Finite Volume Measures
We investigate the following questions: Given a measure μ Λ on configurations on a subset Λ of a lattice L , where a configuration is an element of Ω Λ for some fixed set Ω , does there exist a measure μ on configurations on all of L , invariant under some specified symmetry group of L , such that μ...
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| Veröffentlicht in: | Journal of statistical physics 2017-02, Vol.166 (3-4), p.765-782 |
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| container_title | Journal of statistical physics |
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| creator | Goldstein, S. Kuna, T. Lebowitz, J. L. Speer, E. R. |
| description | We investigate the following questions: Given a measure
μ
Λ
on configurations on a subset
Λ
of a lattice
L
, where a configuration is an element of
Ω
Λ
for some fixed set
Ω
, does there exist a measure
μ
on configurations on all of
L
, invariant under some specified symmetry group of
L
, such that
μ
Λ
is its marginal on configurations on
Λ
? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which
L
=
Z
d
and the symmetries are the translations. For the case in which
Λ
is an interval in
Z
we give a simple necessary and sufficient condition,
local translation invariance
(
LTI
), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which
L
is the Bethe lattice. On
Z
we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When
Λ
⊂
Z
is not an interval, or when
Λ
⊂
Z
d
with
d
>
1
, the LTI condition is necessary but not sufficient for extendibility. For
Z
d
with
d
>
1
, extendibility is in some sense undecidable. |
| doi_str_mv | 10.1007/s10955-016-1595-8 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_1880776397</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A551029400</galeid><sourcerecordid>A551029400</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-df1550ecc5fd132732622bc7d6e67a6c1f934ec65a665439bed2bd0b5f5f55f83</originalsourceid><addsrcrecordid>eNp1kEFLAzEQhYMoWKs_wNuC562T7E6y8VZK1ULFS_UastmkbNlma7IV_femrAcv8g4Dw3szj4-QWwozCiDuIwWJmAPlOUWJeXVGJhQFyyWnxTmZADCWl4LiJbmKcQcAspI4IQ-boH3s9ND2Plv5Tx1a7Yds-TVYH9MuZr3LHlvfDjZ777vj3mYvVsdjsPGaXDjdRXvzO6fk7XG5WTzn69en1WK-zk2BOOSNo4hgjUHX0IKJgnHGaiMabrnQ3FAni9IajppzLAtZ24bVDdToktBVxZTcjXcPof842jioXX8MPr1UtKpACF5IkVyz0bXVnVWtd_0QtElq7L41vbeuTfs5IgUmS4AUoGPAhD7GYJ06hHavw7eioE5M1chUJabqxFSdqrAxE5PXb234U-Xf0A-LSHi9</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1880776397</pqid></control><display><type>article</type><title>Translation Invariant Extensions of Finite Volume Measures</title><source>SpringerLink Journals</source><creator>Goldstein, S. ; Kuna, T. ; Lebowitz, J. L. ; Speer, E. R.</creator><creatorcontrib>Goldstein, S. ; Kuna, T. ; Lebowitz, J. L. ; Speer, E. R.</creatorcontrib><description>We investigate the following questions: Given a measure
μ
Λ
on configurations on a subset
Λ
of a lattice
L
, where a configuration is an element of
Ω
Λ
for some fixed set
Ω
, does there exist a measure
μ
on configurations on all of
L
, invariant under some specified symmetry group of
L
, such that
μ
Λ
is its marginal on configurations on
Λ
? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which
L
=
Z
d
and the symmetries are the translations. For the case in which
Λ
is an interval in
Z
we give a simple necessary and sufficient condition,
local translation invariance
(
LTI
), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which
L
is the Bethe lattice. On
Z
we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When
Λ
⊂
Z
is not an interval, or when
Λ
⊂
Z
d
with
d
>
1
, the LTI condition is necessary but not sufficient for extendibility. For
Z
d
with
d
>
1
, extendibility is in some sense undecidable.</description><identifier>ISSN: 0022-4715</identifier><identifier>EISSN: 1572-9613</identifier><identifier>DOI: 10.1007/s10955-016-1595-8</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Finite volume method ; Mathematical and Computational Physics ; Physical Chemistry ; Physics ; Physics and Astronomy ; Quantum Physics ; Statistical Physics and Dynamical Systems ; Theoretical</subject><ispartof>Journal of statistical physics, 2017-02, Vol.166 (3-4), p.765-782</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>COPYRIGHT 2017 Springer</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-df1550ecc5fd132732622bc7d6e67a6c1f934ec65a665439bed2bd0b5f5f55f83</citedby><cites>FETCH-LOGICAL-c355t-df1550ecc5fd132732622bc7d6e67a6c1f934ec65a665439bed2bd0b5f5f55f83</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/s10955-016-1595-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10955-016-1595-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Goldstein, S.</creatorcontrib><creatorcontrib>Kuna, T.</creatorcontrib><creatorcontrib>Lebowitz, J. L.</creatorcontrib><creatorcontrib>Speer, E. R.</creatorcontrib><title>Translation Invariant Extensions of Finite Volume Measures</title><title>Journal of statistical physics</title><addtitle>J Stat Phys</addtitle><description>We investigate the following questions: Given a measure
μ
Λ
on configurations on a subset
Λ
of a lattice
L
, where a configuration is an element of
Ω
Λ
for some fixed set
Ω
, does there exist a measure
μ
on configurations on all of
L
, invariant under some specified symmetry group of
L
, such that
μ
Λ
is its marginal on configurations on
Λ
? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which
L
=
Z
d
and the symmetries are the translations. For the case in which
Λ
is an interval in
Z
we give a simple necessary and sufficient condition,
local translation invariance
(
LTI
), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which
L
is the Bethe lattice. On
Z
we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When
Λ
⊂
Z
is not an interval, or when
Λ
⊂
Z
d
with
d
>
1
, the LTI condition is necessary but not sufficient for extendibility. For
Z
d
with
d
>
1
, extendibility is in some sense undecidable.</description><subject>Finite volume method</subject><subject>Mathematical and Computational Physics</subject><subject>Physical Chemistry</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Statistical Physics and Dynamical Systems</subject><subject>Theoretical</subject><issn>0022-4715</issn><issn>1572-9613</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLAzEQhYMoWKs_wNuC562T7E6y8VZK1ULFS_UastmkbNlma7IV_femrAcv8g4Dw3szj4-QWwozCiDuIwWJmAPlOUWJeXVGJhQFyyWnxTmZADCWl4LiJbmKcQcAspI4IQ-boH3s9ND2Plv5Tx1a7Yds-TVYH9MuZr3LHlvfDjZ777vj3mYvVsdjsPGaXDjdRXvzO6fk7XG5WTzn69en1WK-zk2BOOSNo4hgjUHX0IKJgnHGaiMabrnQ3FAni9IajppzLAtZ24bVDdToktBVxZTcjXcPof842jioXX8MPr1UtKpACF5IkVyz0bXVnVWtd_0QtElq7L41vbeuTfs5IgUmS4AUoGPAhD7GYJ06hHavw7eioE5M1chUJabqxFSdqrAxE5PXb234U-Xf0A-LSHi9</recordid><startdate>20170201</startdate><enddate>20170201</enddate><creator>Goldstein, S.</creator><creator>Kuna, T.</creator><creator>Lebowitz, J. L.</creator><creator>Speer, E. R.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170201</creationdate><title>Translation Invariant Extensions of Finite Volume Measures</title><author>Goldstein, S. ; Kuna, T. ; Lebowitz, J. L. ; Speer, E. R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-df1550ecc5fd132732622bc7d6e67a6c1f934ec65a665439bed2bd0b5f5f55f83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Finite volume method</topic><topic>Mathematical and Computational Physics</topic><topic>Physical Chemistry</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Statistical Physics and Dynamical Systems</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Goldstein, S.</creatorcontrib><creatorcontrib>Kuna, T.</creatorcontrib><creatorcontrib>Lebowitz, J. L.</creatorcontrib><creatorcontrib>Speer, E. R.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of statistical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Goldstein, S.</au><au>Kuna, T.</au><au>Lebowitz, J. L.</au><au>Speer, E. R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Translation Invariant Extensions of Finite Volume Measures</atitle><jtitle>Journal of statistical physics</jtitle><stitle>J Stat Phys</stitle><date>2017-02-01</date><risdate>2017</risdate><volume>166</volume><issue>3-4</issue><spage>765</spage><epage>782</epage><pages>765-782</pages><issn>0022-4715</issn><eissn>1572-9613</eissn><abstract>We investigate the following questions: Given a measure
μ
Λ
on configurations on a subset
Λ
of a lattice
L
, where a configuration is an element of
Ω
Λ
for some fixed set
Ω
, does there exist a measure
μ
on configurations on all of
L
, invariant under some specified symmetry group of
L
, such that
μ
Λ
is its marginal on configurations on
Λ
? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which
L
=
Z
d
and the symmetries are the translations. For the case in which
Λ
is an interval in
Z
we give a simple necessary and sufficient condition,
local translation invariance
(
LTI
), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which
L
is the Bethe lattice. On
Z
we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When
Λ
⊂
Z
is not an interval, or when
Λ
⊂
Z
d
with
d
>
1
, the LTI condition is necessary but not sufficient for extendibility. For
Z
d
with
d
>
1
, extendibility is in some sense undecidable.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10955-016-1595-8</doi><tpages>18</tpages></addata></record> |
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| ispartof | Journal of statistical physics, 2017-02, Vol.166 (3-4), p.765-782 |
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| language | eng |
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| source | SpringerLink Journals |
| subjects | Finite volume method Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| title | Translation Invariant Extensions of Finite Volume Measures |
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