The Poisson boundary of the projected simple symmetric random walk on Thompson's group F is the skeleton end boundary, with hitting measure a biased Bernoulli product on odd 2-adic integers that is singular to Haar measure but exact-dimensional.
Some graphs related to Thompson's group F
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The Schreier graphs of Thompson's group F with respect to the stabilizer of 1/2 and generators x_0 and x_1, and of its unitary representation in L_2([0,1]) induced by the standard action on the interval [0,1] are explicitly described. The coamenability of the stabilizers of any finite set of dyadic rational numbers is established. The induced subgraph of the right Cayley graph of the positive monoid of F containing all the vertices of the form x_nv, where n>=0 and v is any word over the alphabet {x_0, x_1}, is constructed. It is proved that the latter graph is non-amenable.
verdicts
UNVERDICTED 2representative citing papers
Extends a superharmonic-function amenability test to group actions and applies it to Thompson's group F without resolving amenability.
citing papers explorer
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The one-point Schreier Poisson boundary of Thompson's group $F$
The Poisson boundary of the projected simple symmetric random walk on Thompson's group F is the skeleton end boundary, with hitting measure a biased Bernoulli product on odd 2-adic integers that is singular to Haar measure but exact-dimensional.