论文标题
沿树木的向后的千古定理及其对自由小组动作的后果
A backward ergodic theorem along trees and its consequences for free group actions
论文作者
论文摘要
我们证明了一种新的偏角定理，用于概率 - 估计性构成（PMP）的自由组动作，其中沿着扎根于身份的标准cayley图的任意有限子树取出了ergodic平均值。该结果是Grigorchuk（1987）和Nevo and Stein（1994）的理论的显着加强，它的版本是Bufetov于2002年猜想的。我们的自由群体的定理是由一个新的 - 向后的 - 偏僻的 - ergodic -ergodic Theorem，用于可计时的PMP转换，在该处，该pmp转换是超过仲裁的次要树，i. i i i i.过去）。我们还讨论了该向后定理的其他应用，特别是在Markov措施中，在移位图上，该应用沿树沿树的边界动作产生了一个方向的千古定理。
We prove a new pointwise ergodic theorem for probability-measure-preserving (pmp) actions of free groups, where the ergodic averages are taken over arbitrary finite subtrees of the standard Cayley graph rooted at the identity. This result is a significant strengthening of a theorem of Grigorchuk (1987) and Nevo and Stein (1994), and a version of it was conjectured by Bufetov in 2002. Our theorem for free groups arises from a new - backward - ergodic theorem for a countable-to-one pmp transformation, where the averages are taken over arbitrary trees of finite height in the backward orbit of the point (i.e. trees of possible pasts). We also discuss other applications of this backward theorem, in particular to the shift map with Markov measures, which yields a pointwise ergodic theorem along trees for the boundary actions of free groups.
