论文标题
在小组和公里国家随机行走
Random walks on groups and KMS states
论文作者
论文摘要
经典的建筑与离散组$γ$ a compact $γ$ -space $ \partial_mγ$的瞬态随机步行相结合，称为马丁边界。由此产生的交叉产品$ c^*$ - 代数$ c（\partial_mγ）\rtimes_rγ$配备了由Martin内核给出的单参数的一组自动形态，这些自动形态定义了马丁边界。在本文中，我们研究了KMS的流量状态，并在随机行走的泊松边界微不足道并且$γ$是无扭转的非质量非质量双曲线群时获得完整的描述。我们还构建了示例，以表明除这些情况外，KMS状态的结构可能更加复杂。
A classical construction associates to a transient random walk on a discrete group $Γ$ a compact $Γ$-space $\partial_M Γ$ known as the Martin boundary. The resulting crossed product $C^*$-algebra $C(\partial_M Γ) \rtimes_r Γ$ comes equipped with a one-parameter group of automorphisms given by the Martin kernels that define the Martin boundary. In this paper we study the KMS states for this flow and obtain a complete description when the Poisson boundary of the random walk is trivial and when $Γ$ is a torsion free non-elementary hyperbolic group. We also construct examples to show that the structure of the KMS states can be more complicated beyond these cases.
