Renaud Leplaideur 2005 Nonlinearity 18 2847 doi:10.1088/0951-7715/18/6/023
A dynamical proof for the convergence of Gibbs measures at temperature zero
Renaud Leplaideur
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We give a dynamical proof of a result due to Brémont (2003 Nonlinearity 16 419–26). It concerns the problem of maximizing measures for some given observable 
: for a subshift of finite type, and when only depends on a finite number of coordinates, it was proved in Brémont (2003) that the unique equilibrium state associated with β converges to some measure when β goes to +∞. This measure has maximal entropy among the maximizing measures for . We give here a dynamical proof of this result and we improve it. We prove that for any Hölder continuous function (not necessarily locally constant), f, the unique equilibrium state associated with f + β converges to some measure with maximal f-pressure among the maximizing measures. Moreover we also identify the limit measure.
- PACS
- MSC
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37A60 Dynamical systems in statistical mechanics (See also 82Cxx)
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
- Subjects
- Dates
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Issue 6 (November 2005)
Received 12 January 2005, in final form 31 August 2005
Published 14 October 2005
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A dynamical proof for the convergence of Gibbs measures at temperature zero
Renaud Leplaideur 2005 Nonlinearity 18 2847
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