相关论文: Partitions with independent iterates in random dyn…

We exhibit rationally ergodic, weakly mixing measure preserving transformations which are not subsequence rationally weakly mixing and give a condition for smoothness of renewal sequences.

For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the formally stronger finite type property of Ngai and Wang. We…

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…

We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of…

Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under…

High-multiplicity Kepler systems (referred to as Kepler multis) are often tightly packed and may be on the verge of instability. Many systems of this type could have experienced past instabilities, where the compact orbits and often low…

A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…

We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…

The converse of the Borel-Cantelli Lemma states that if $\{A_i\}_{i=1}^\infty$ is a sequence of independent events such that $\sum P(A_i)=\infty$, then almost surely infinitely many of these events will occur. Erd\H os and R\'enyi proved…

We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…

We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age…

Exploiting the azimuthal angle dependence of the density matrices we construct observables that directly measure the spin of a heavy unstable particle. A novelty of the approach is that the analysis of the azimuthal angle dependence in a…

We examine some of the properties of uniformly rigid transformations, and analyze the compatibility of uniform rigidity and (measurable) weak mixing along with some of their asymptotic convergence properties. We show that on Cantor space,…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…

In this paper, we prove a large deviation principle for the empirical measures of a system of weakly interacting diffusion with reflection. We adopt the weak convergence approach. To make this approach work, we show that the sequence of…

We investigate a particular form of weak convergence of the local empirical process.

Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in [22]. In this paper we continue to investigate this notion. In particular, we prove that all dynamical…

For each $n \geq 1$, let $\{X_{j,n}\}_{1 \leq j \leq n}$ be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process…

A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but non-positive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems. The…