论文标题
无限的DLR测量和体积类型的相变
Infinite DLR Measures and Volume-Type Phase Transitions on Countable Markov Shifts
论文作者
论文摘要
我们考虑在$σ$ -Finite量度上的Markov Shifts的$σ$ finite措施中的自然定义。我们证明，DLR度量集包含与Walters电位相关的一组共形度量。在BIP案例中，或者当电势使Ruelle的操作员归一化时，我们证明了DLR和共形的概念一致。在标准更新转移时，我们研究了描述征征分别从有限的措施跳到无限措施的案例的问题，当我们考虑高温和低温时。对于这种特定的转变，我们证明始终存在有限的DLR度量，并且我们对这种体积类型相变的临界温度表达，这仅针对具有无限第一变化的电势。
We consider the natural definition of DLR measure in the setting of $σ$-finite measures on countable Markov shifts. We prove that the set of DLR measures contains the set of conformal measures associated with Walters potentials. In the BIP case, or when the potential normalizes the Ruelle's operator, we prove that the notions of DLR and conformal coincide. On the standard renewal shift, we study the problem of describing the cases when the set of the eigenmeasures jumps from finite to infinite measures when we consider high and low temperatures, respectively. For this particular shift, we prove that there always exist finite DLR measures, and we have an expression to the critical temperature for this volume-type phase transition, which occurs only for potentials with the infinite first variation.
