The ratio set of the harmonic measure of a random walk on a hyperbolic group
The ratio set of the harmonic measure of a random walk on a hyperbolic group
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DOI：
10.1007/s11856-008-0013-6
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发表时间：
2006-02
影响因子：
1
通讯作者：
Masaki Izumi;S. Neshveyev;Rui Okayasu
中科院分区：
文献类型：
--
作者：
Masaki Izumi;S. Neshveyev;Rui Okayasu
本文研究了一类由有限值域随机游动定义的非顺从双曲群的Gromov边界上的调和测度，并研究了边界上相应的轨道等价关系.已知它总是顺从的并且是III型的。我们确定其比率集表明，它是由马丁内核的某些值。特别是，我们表明，等价关系是从来没有类型III0。
We consider the harmonic measure on the Gromov boundary of a non-amenable hyperbolic group defined by a finite range random walk on the group, and study the corresponding orbit equivalence relation on the boundary. It is known to be always amenable and of type III. We determine its ratio set by showing that it is generated by certain values of the Martin kernel. In particular, we show that the equivalence relation is never of type III0.