Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensive amenability and an application to interval exchanges   Extensive amenability is a property of group actions which has recently been
used as a tool to prove amenability of groups. We study this property and prove
that it is preserved under a very general construction of semidirect products.
As an application, we establish the amenability of all subgroups of the group
IET of interval exchange transformations that have angular components of
rational rank~${\leq 2}$.
  In addition, we obtain a reformulation of extensive amenability in terms of
inverted orbits and use it to present a purely probabilistic proof that
recurrent actions are extensively amenable. Finally, we study the triviality of
the Poisson boundary for random walks on IET and show that there are subgroups
$G <IET$ admitting no finitely supported measure with trivial boundary.

15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an