相关论文: Poisson boundary of group extensions

Using the language of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is then used to obtain an explicit…

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.

We propose a consistent set of boundary conditions for gravity in asymptotically flat spacetime at spacelike infinity, which yields an enhancement of the Bondi-Metzner Sachs group with smooth superrotations and new subleading symmetries.…

Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…

We consider the simple random walk on the infinite cluster of the Bernoulli bond percolation of trees, and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…

Consider $\operatorname{Sym}(n)$, endowed with the normalized Hamming metric $d_n$. A finitely-generated group $\Gamma$ is \emph{P-stable} if every almost homomorphism $\rho_{n_k}\colon \Gamma\rightarrow\operatorname{Sym}(n_k)$ (i.e., for…

We establish the theorems that give necessary and sufficient conditions for an arbitrary function defined in the unit disk of complex plane in order to has boundary values along classes of equivalencies of simple curves. Our results…

We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…

A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…

Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…

The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes…

We determine the range of Furstenberg entropy for stationary ergodic actions of nonabelian free groups by an explicit construction involving random walks on random coset spaces.

It is shown that the operator space generated by peripheral eigenvectors of a unital completely positive map on a von Neumann algebra has a $C^*$-algebra structure. This extends the notion of non-commutative Poisson boundary by including…

We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

This paper investigates coherent-like conditions and related properties that a trivial extension might inherit from the ground ring over some classes of modules. It captures previous results dealing primarily with coherence, and also…

In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field…