Zero Temperature Limits of Gibbs Equilibrium States for Countable Markov Shifts
We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states μ tf for all t , the measures μ tf converge in the weak star topology as t tends to infinity.
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| Published in | Journal of statistical physics Vol. 143; no. 4; pp. 795 - 806 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.05.2011
Springer |
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| Abstract | We prove that, given a uniformly locally constant potential
f
on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states
μ
tf
for all
t
, the measures
μ
tf
converge in the weak star topology as
t
tends to infinity. |
|---|---|
| AbstractList | We prove that, given a uniformly locally constant potential
f
on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states
μ
tf
for all
t
, the measures
μ
tf
converge in the weak star topology as
t
tends to infinity. We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states [[mu].sub.tf] for all t, the measures [[mu].sub.tf] converge in the weak star topology as t tends to infinity. Keywords Gibbs state * Equilibrium state * Maximizing measure * Countable alphabet Markov shift |
| Audience | Academic |
| Author | Kempton, Tom |
| Author_xml | – sequence: 1 givenname: Tom surname: Kempton fullname: Kempton, Tom email: t.kempton@warwick.ac.uk organization: Mathematics Department, University of Warwick |
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| Cites_doi | 10.1002/9780470316962 10.1007/BF02773377 10.1017/S014338570600040X 10.1090/S0002-9939-03-06927-2 10.1088/0951-7715/18/6/023 10.1007/s00605-005-0389-x 10.1017/S014338571000026X 10.1017/S0143385799146820 10.1007/s10955-005-3035-z 10.1088/0951-7715/16/2/303 10.1007/s10955-006-9215-7 10.1007/s00220-010-0997-8 10.1017/CBO9780511543050 |
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| Keywords | Equilibrium state Countable alphabet Markov shift Maximizing measure Gibbs state |
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| References_xml | – volume-title: Convergence of Probability Measures year: 1999 ident: 195_CR2 doi: 10.1002/9780470316962 contributor: fullname: P. Billingsley – volume: 125 start-page: 93 year: 2001 ident: 195_CR11 publication-title: Isr. J. Math. doi: 10.1007/BF02773377 contributor: fullname: R.D. Mauldin – volume: 26 start-page: 1791 issue: 6 year: 2006 ident: 195_CR9 publication-title: Ergod. Theory Dyn. Syst. doi: 10.1017/S014338570600040X contributor: fullname: O. Jenkinson – volume: 131 start-page: 1751 issue: 6 year: 2003 ident: 195_CR15 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-03-06927-2 contributor: fullname: O. Sarig – volume: 18 start-page: 2847 issue: 6 year: 2005 ident: 195_CR10 publication-title: Nonlinearity doi: 10.1088/0951-7715/18/6/023 contributor: fullname: R. Leplaideur – volume: 150 start-page: 91 issue: 2 year: 2007 ident: 195_CR7 publication-title: Monatshefte Math. doi: 10.1007/s00605-005-0389-x contributor: fullname: G. Iommi – ident: 195_CR1 – ident: 195_CR5 doi: 10.1017/S014338571000026X – volume: 19 start-page: 1565 issue: 6 year: 1999 ident: 195_CR14 publication-title: Ergod. Theory Dyn. Syst. doi: 10.1017/S0143385799146820 contributor: fullname: O. Sarig – ident: 195_CR6 – volume: 119 start-page: 765 issue: 3–4 year: 2005 ident: 195_CR8 publication-title: J. Stat. Phys. doi: 10.1007/s10955-005-3035-z contributor: fullname: O. Jenkinson – volume: 16 start-page: 419 issue: 2 year: 2003 ident: 195_CR3 publication-title: Nonlinearity doi: 10.1088/0951-7715/16/2/303 contributor: fullname: J. Brémont – volume: 126 start-page: 315 issue: 2 year: 2007 ident: 195_CR13 publication-title: J. Stat. Phys. doi: 10.1007/s10955-006-9215-7 contributor: fullname: I.D. Morris – volume: 297 start-page: 265 issue: 1 year: 2010 ident: 195_CR4 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-010-0997-8 contributor: fullname: J.-R. Chazottes – volume-title: Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets year: 2003 ident: 195_CR12 doi: 10.1017/CBO9780511543050 contributor: fullname: R.D. Mauldin |
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| Snippet | We prove that, given a uniformly locally constant potential
f
on a countable state Markov shift and suitable conditions which guarantee the existence of the... We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the... |
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| SubjectTerms | Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| Title | Zero Temperature Limits of Gibbs Equilibrium States for Countable Markov Shifts |
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