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 ≤ 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.

A generalized likelihood ratio test (GLRT) is derived for adaptive detection of range and Doppler-distributed targets. The clutter is modeled as a spherically invariant random process (SIRP) and its texture component is range dependent (heterogeneous clutter). We suppose here that the speckle component covariance matrix is known or estimated thanks to a secondary data set. Thus, unknown parameters to be estimated are local texture values, the complex amplitudes and Doppler frequencies of all scattering centers. To do so, we use superresolution methods. The proposed detector assumes a priori knowledge on the spatial distribution of the target and has the precious property of having a constant false alarm rate (CFAR) with the assumption of a known speckle covariance matrix or by the use of frequency agility.

We study the uniformly recurrent subgroups of groups acting by homeomorphisms on a topological space. We prove a general result relating uniformly recurrent subgroups to rigid stabilizers of the action, and deduce a C * -simplicity criterion based on the non-amenability of rigid stabilizers. As an application, we show that Thompson's group V is C * -simple, as well as groups of piecewise projective homeomorphisms of the real line. This provides examples of finitely presented C * -simple groups without free subgroups. We prove that a branch group is either amenable or C * -simple. We also prove the converse of a result of Haagerup and Olesen: if Thompson's group F is non-amenable, then Thompson's group T must be C * -simple. Our results further provide sufficient conditions on a group of homeomorphisms under which uniformly recurrent subgroups can be completely classified. This applies to Thompson's groups F , T and V , for which we also deduce rigidity results for their minimal actions on compact spaces.