相关论文: Limit laws for distorted return time processes for…

We investigate quantitative recurrence in systems having an infinite measure. We extend the Ornstein-Weiss theorem for a general class of infinite systems estimating return time in decreasing sequences of cylinders. Then we restrict to a…

We define a random walk adic transformation associated to an aperiodic random walk on $G=\mathbb{Z}^{k}\times\mathbb{R}^{D-k}$ driven by a $\beta$-transformation and study its ergodic properties. In particular, this transformation is…

We prove that ergodic measures on one-sided shift spaces are uniformly scaling in the sense of Gavish. That is, given a shift ergodic measure we prove that at almost every point the scenery distributions weakly converge to a common…

We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics. We connect these observations with the exact integrability…

We define an infinite measure-preserving transformation to have infinite symmetric ergodic index if all finite Cartesian products of the transformation and its inverse are ergodic, and show that infinite symmetric ergodic index does not…

We compare ergodic properties of the kinetic energy for three stochastic models of subrecoil-laser-cooled gases. One model is based on a heterogeneous random walk (HRW), another is an HRW with long-range jumps (the exponential model), and…

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…

We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this…

We investigate some asymptotic properties of general Markov processes conditioned not to be absorbed by moving boundaries. We first give general criteria involving an exponential convergence towards the Q-process, that is the law of the…

We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…

We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without…

In the paradigmatic example of quantum measurements, whenever one measures a system which starts in a superposition of two states of a conserved quantity, it jumps to one of the two states, implying different final values for the quantity…

We prove that the joint distribution of the occupation time ratios for ergodic transformations preserving an infinite measure converges to a multidimensional version of Lamperti's generalized arcsine distribution, in the sense of strong…

We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in…

We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergence of the regularized solutions toward discontinuous…

We give examples of rank-one transformations that are (weak) doubly ergodic and rigid (so all their cartesian products are conservative), but with non-ergodic $2$-fold cartesian product. We give conditions for rank-one infinite…

We prove a general ergodic-theoretic result concerning the return time statistic, which, properly understood, sheds some new light on the common sense phenomenon known as {\it the law of series}. Let \proc be an ergodic process on finitely…

We analyze the entangling capabilities of unitary transformations $U$ acting on a bipartite $d_1\times d_2$-dimensional quantum system. To this aim we introduce an entangling power measure $e(U)$ given by the mean linear entropy produced…

Weakly chaotic non-linear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and non-integrable observables remain random even in the long time limit. Temporal averages of integrable observables…

Kac's lemma determines the expected return time to a set of positive measure under iterations of an ergodic probability preserving transformations. We introduce the notion of an \emph{allocation} for a probability preserving action of a…