A dynamical proof for the convergence of Gibbs measures at temperature zero
A dynamical proof for the convergence of Gibbs measures at temperature zero
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零温下吉布斯测度收敛的动力学证明
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发表时间：
2005
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通讯作者：
R. Leplaideur
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作者：
R. Leplaideur
我们给出了Brémont（2003 Nonlinearity 16 419-26）的一个结果的动力学证明。它涉及到对给定的可观测的β的最大化测度的问题：对于有限类型的子移位，当β仅依赖于有限个坐标时，Brémont（2003）证明了当β趋于+∞时，与β β相关的唯一平衡态收敛于某个测度。该测度在最大化测度中具有最大熵。本文给出了这一结果的动力学证明并改进了它，证明了对任意Hölder连续函数（不一定是局部常数）f，与f + β相关联的唯一平衡态收敛于极大化测度中具有最大f-压力的某个测度.此外，我们还确定了极限测度。
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 ϕ: for a subshift of finite type, and when ϕ only depends on a finite number of coordinates, it was proved in Brémont (2003) that the unique equilibrium state associated with βϕ converges to some measure when β goes to +∞. This measure has maximal entropy among the maximizing measures for ϕ. 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 + βϕ converges to some measure with maximal f-pressure among the maximizing measures. Moreover we also identify the limit measure.