相对（τ）、扩张器与某些扩张映射的相关性衰减
Relative ($τ$), Expanders, and Decay of Correlations for certain Expanding Maps
- Durham University（杜伦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究探究结构较简单的扩张动力系统有限片覆盖塔是否存在与模曲面同余覆盖族类似的指数混合现象，运用转移算子工具并与Cuntz-Krieger代数KMS态建立联系。
AI中文摘要：
相对（τ）等价于群商Γ_q=Γ/N_q（q∈ℕ）对应的凯莱图序列构成扩张器族的命题。存在一种观点认为扩张器图可产生良好的混合性；例如，源于SL(2,ℝ)作用的对称性及拉普拉斯算子的一致谱隙，模曲面的同余覆盖族上的测地流具有指数混合性。我们在结构更简单的情形中探究是否存在类似现象，针对某些扩张动力系统的有限片覆盖塔展开研究。我们运用尤其适用于有限型子转移映射和区间扩张映射情形的转移算子工具，并与Cuntz-Krieger代数的KMS态建立了富有成效的联系。
英文摘要：
Relative ($τ$) is equivalent to a statement that the sequence of Cayley graphs associated to group quotients $Γ_q=Γ/N_q$, $q\in\mathbb{N}$, form an expander family. There is a philosophy that expander graphs give rise to good mixing; for instance, one has exponential mixing for the geodesic flow uniformly the along a family of congruence covers of the modular surface, stemming from the symmetry in the $\mathrm{SL}(2,\mathbb{R})$ action and the uniform spectral gap for the Laplacian. Do we see similar phenomena in less structured settings? We investigate this question for a tower of finite sheeted covers of certain expanding dynamical systems. We use transfer operator machinery that applies in particular in the cases of subshifts of finite type and expanding interval maps. We make fruitful connections with KMS states of Cuntz--Krieger algebras.
