Kempton, Tom. (2011) Zero temperature limits of Gibbs equilibrium states for countable Markov shifts. Journal of Statistical Physics, Vol.143 (No.4). pp. 795-806. ISSN 0022-4715

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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 mu(tf) for all t, the measures mu(tf) converge in the weak star topology as t tends to infinity.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Equilibrium, Gibbs' equation, Markov processes
Journal or Publication Title:	Journal of Statistical Physics
Publisher:	Springer New York LLC
ISSN:	0022-4715
Date:	2011
Volume:	Vol.143
Number:	No.4
Page Range:	pp. 795-806
Identification Number:	10.1007/s10955-011-0195-x
Status:	Peer Reviewed
Publication Status:	Published
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
References:	1. Baraviera, A.T., Leplaideur, R., Lopes, A.O.: Selection of measures for a potential with two maxima at the zero temperature limit. ArXiv e-prints (April 2010) 2. Billingsley, P.: Convergence of Probability Measures, 2nd edn.Wiley Series in Probability and Statistics. Wiley, New York (1999). A Wiley-Interscience Publication 3. Brémont, J.: Gibbs measures at temperature zero. Nonlinearity 16(2), 419–426 (2003) 4. Chazottes, J.-R., Hochman, M.: On the zero-temperature limit of Gibbs states. Commun. Math. Phys. 297(1), 265–281 (2010) 5. Chazottes, J.R., Gambaudo, J.M., Ugalde, E.: Zero-temperature limit of one-dimensional Gibbs states via renormalization: the case of locally constant potentials (2009) 6. Coelho, Z.N.: Entropy and ergodicity of skew-products over subshifts of finite type and central limit asymptotics. PhD thesis, University of Warwick (1990) 7. Iommi, G.: Ergodic optimization for renewal type shifts. Monatshefte Math. 150(2), 91–95 (2007) 8. Jenkinson, O., Mauldin, R.D., Urba´nski, M.: Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type. J. Stat. Phys. 119(3–4), 765–776 (2005) 9. Jenkinson, O., Mauldin, R.D., Urba´nski, M.: Ergodic optimization for countable alphabet subshifts of finite type. Ergod. Theory Dyn. Syst. 26(6), 1791–1803 (2006) 10. Leplaideur, R.: A dynamical proof for the convergence of Gibbs measures at temperature zero. Nonlinearity 18(6), 2847–2880 (2005) 11. Mauldin, R.D., Urba´nski, M.: Gibbs states on the symbolic space over an infinite alphabet. Isr. J. Math. 125, 93–130 (2001) 12. Mauldin, R.D., Urba´nski, M.: Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets. Cambridge Tracts in Mathematics, vol. 148. Cambridge University Press, Cambridge (2003) 13. Morris, I.D.: Entropy for zero-temperature limits of Gibbs-equilibrium states for countable-alphabet subshifts of finite type. J. Stat. Phys. 126(2), 315–324 (2007) 14. Sarig, O.: Thermodynamic formalism for countable Markov shifts. Ergod. Theory Dyn. Syst. 19(6), 1565–1593 (1999) 15. Sarig, O.: Existence of Gibbs measures for countable Markov shifts. Proc. Am.Math. Soc. 131(6), 1751– 1758 (2003) (electronic)
URI:	http://wrap.warwick.ac.uk/id/eprint/39975

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