论文标题
由稳定的随机场的混合特性，由正交和双曲线组索引
Mixing Properties of Stable Random Fields Indexed by Amenable and Hyperbolic Groups
论文作者
论文摘要
我们表明，任何固定的符号$α$ stable（$sαs$）随机字段由可数的木材$ g $索引时，仅当且仅当其由无效的动作产生时，就会扩展Samorodnitsky和Wang-Roy-Sto的作品，并将Abelian组的作品扩展到Abelian for Abelian for Abelian for Abelian for Abelable组。这使我们能够显着改善最近发现的与冯·诺伊曼代数的联系的领域。我们还建立了与边界和双重边界$ g $相关的固定$sαs$场的奇迹性，其中边界配备了帕特森·苏利文（Patterson-Sullivan）或随机步行的命中量，并且双边界配备了Bowen-Margulis-Sullivan量度。
We show that any stationary symmteric $α$-stable ($SαS$) random field indexed by a countable amenable group $G$ is weakly mixing if and only if it is generated by a null action, extending works of Samorodnitsky and Wang-Roy-Stoev for abelian groups to all amenable groups. This enables us to improve significantly the domain of a recently discovered connection to von Neumann algebras. We also establish ergodicity of stationary $SαS$ fields associated with boundary and double boundary actions of a hyperbolic group $G$, where the boundary is equipped with either the Patterson-Sullivan or the hitting measure of a random walk, and the double boundary is equipped with the Bowen-Margulis-Sullivan measure.
