论文标题
淬灭和退火的平衡状态，用于随机ruelle扩展地图和应用
Quenched and annealed equilibrium states for random Ruelle expanding maps and applications
论文作者
论文摘要
在本文中，我们描述了作用在波兰空间上的扩展地图的半群的光谱特性，考虑了沿无限动力学和集成转移操作员的两个转移算子的序列。我们证明，这种转移操作员的行为存在限制行为，并且这些半群的行动允许平衡状态具有指数衰减的相关性和几种限制定理。这些结果以淬火和退火的平衡状态对这些结果进行了重新制定，该结果扩展了Baladi（1997）和Carvalho，Rodrigues＆Varandas（2017）的结果，其中随机行走驱动，并假定相位空间是紧凑的。此外，我们证明了淬灭的平衡度量不断变化，并且可以从后者中回收退火的平衡状态。最后，我们在加权的非自主迭代功能系统，自由的半群动作和平衡边界的情况下提供了一些应用。
In this paper we describe the spectral properties of semigroups of expanding maps acting on Polish spaces, considering both sequences of transfer operators along infinite compositions of dynamics and integrated transfer operators. We prove that there exists a limiting behaviour for such transfer operators, and that these semigroup actions admit equilibrium states with exponential decay of correlations and several limit theorems. The reformulation of these results in terms of quenched and annealed equilibrium states extend results by Baladi (1997) and Carvalho, Rodrigues & Varandas (2017), where the randomness is driven by a random walk and the phase space is assumed to be compact. Furthermore, we prove that the quenched equilibrium measures vary Hölder continuously and that the annealed equilibrium states can be recovered from the latter. Finally, we give some applications in the context of weighted non-autonomous iterated function systems, free semigroup actions and on the boundary of equilibria.
