论文标题
平衡状态的零温度极限在拓扑及可数的马尔可夫移位上的存在
Existence of the zero temperature limit of equilibrium states on topologically transitive countable Markov shifts
论文作者
论文摘要
考虑具有有限的Gurevich压力和$ \ Mathrm {var} _1（ϕ）<\ iffty $的拓扑及可计数的马尔可夫移动$σ$和可总结马尔可夫电位$ ϕ $。我们证明了lim $ \ lim_ {t \ to \ infty}μ_t$在弱$^\ star $ topology中的存在，其中$μ_t$是与潜在$ tx $相关的唯一平衡状态。除此之外，我们提出了示例，其中存在零温度的极限，以满足更多一般条件的电势。
Consider a topologically transitive countable Markov shift $Σ$ and a summable Markov potential $ϕ$ with finite Gurevich pressure and $\mathrm{Var}_1(ϕ) < \infty$. We prove existence of the limit $\lim_{t \to \infty} μ_t$ in the weak$^\star$ topology, where $μ_t$ is the unique equilibrium state associated to the potential $tϕ$. Besides that, we present examples where the limit at zero temperature exists for potentials satisfying more general conditions.
