Related papers: Discrete spectrum for amenable group actions

We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then…

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…

In this work we introduce and study a new notion of amenability for actions of locally compact groups on $C^*$-algebras. Our definition extends the definition of amenability for actions of discrete groups due to Claire…

Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.

We analyze the Hamiltonian of the compactified D=11 supermembrane with non-trivial central charge in terms of the matrix model constructed recently by some of the authors. Our main result provides a rigorous proof that the quantum…

This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…

We study the asymptotic behavior of discrete measures on S^{n-1} that are induced by radially projecting point masses concentrated on the integral lattice-points within dilates of a compact body D, for various classes of D. The results…

The asymptotic behaviour of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessarily compact) and connected Riemannian manifolds with…

We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…

We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…

Let $(X,G)$, $(Y,G)$ be two $G$-systems, where $G$ is an infinite countable discrete amenable group and $X$, $Y$ are compact metric spaces. Suppose that $\mathcal{U}$ is a cover of $X$. We first introduce the conditional local topological…

For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…

We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author's conjectures relating definably compact groups $G$…

The harmonic measure $\nu$ on the boundary of the group $Sol$ associated to a discrete random walk of law $\mu$ was described by Kaimanovich. We investigate when it is absolutely continuous or singular with respect to Lebesgue measure. By…

We prove in this note that there is, for some foliated bundles, a bijective correspondance between Garnett's harmonic measures and measures on the fiber that are stationary for some probability measure on the holonomy group. As a…

We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their empirical eigenvalue distribution converges to a limiting…

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.

We introduce a notion of mean cohomological independence dimension for actions of discrete amenable groups on compact metrizable spaces, as a variant of mean dimension, and use it to obtain lower bounds for the radius of comparison of the…

For every non-elementary hyperbolic group, we show that for every random walk with finitely supported admissible step distribution, the associated entropy equals the drift times the logarithmic volume growth if and only if the corresponding…

We prove that a positive-definite measure in $\mathbb{R}^n$ with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent…