Related papers: Discrete spectrum for amenable group actions
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any…
Let L be a countable language. We say that a countable infinite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set as M that is invariant under…
We generalize Berg's notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure preserving system. As a corollary we obtain easy to check necessary and…
We initiate a systematic investigation of group actions on compact medain algebras via the corresponding dynamics on their spaces of measures. We show that a probability measure which is invariant under a natural push forward operation must…
A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
To each finitely generated group $G$, we associate a quasi-isometric invariant called the \emph{Dehn spectrum} of $G$. If $G$ is finitely presented, our invariant is closely related to the Dehn function of $G$, but provides more information…
Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
We introduce the notion of hyperfiniteness for permutation actions of countable groups on countable sets and give a geometric and analytic characterization, similar to the known characterizations for amenable actions. We also answer a…
Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…
We determine when contractive idempotents in the measure algebra of a locally compact group commute. We consider a dynamical version of the same result. We also look at some properties of groups of measures whose identity is a contactive…
We give improvements of estimates of invariant metrics in the normal direction on strictly pseudoconvex domains. Specifically we will give the second term in the expansion of the metrics. This depends on an improved localisation result and…
We propose another proof of the high dimensional spectrum convergence of the weighted sample covariance, more concise and self-sufficient but with stronger, but reasonable assumptions. We explain and illustrates this theorem for different…
We prove that if G is a discrete group that admits a metrically proper action on a finite-dimensional CAT(0) cube complex X, then G is weakly amenable. We do this by constructing uniformly bounded Hilbert space representations for which the…
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are…
It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Cech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete…
A measure on a locally compact Abelian group is said to have a natural spectrum if its spectrum is equal to the closure of the range of the Fourier-Stieltjes transform. In this paper we continue the study of spectrally reasonable measures…