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N. Fournier and A. Guillin obtained in their 2015 PTRF paper some bounds of the L^p-mean rate of convergence in Wasserstein distance of empirical distributions for a class of stationary mixing processes. In this paper, we propose to extend…

We prove functional, distributional limit theorems for the occupation times of pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting processes are tied down Mittag-Leffler processes and the…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

We prove distributional limit theorems (conditional and integrated) for the occupation times of certain weakly mixing, pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting random variables…

In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation…

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed…

We consider conservative ergodic measure preserving transformations on infinite measure spaces and investigate the asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition. We…

We prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$, assuming that each map $T_i$ and each pair $T_iT_j^{-1}$ is ergodic for $i\neq j$. The limiting behavior of such…

In infinite ergodic theory, two distributional limit theorems are well-known. One is characterized by the Mittag-Leffler distribution for time averages of $L^1(m)$ functions, i.e., integrable functions with respect to an infinite invariant…

We consider a particle diffusing along the links of a general graph possessing some absorbing vertices. The particle, with a spatially-dependent diffusion constant D(x) is subjected to a drift U(x) that is defined in every point of each…

We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows…

We prove the norm convergence of multiple ergodic averages along cubes for several commuting transformations, and derive corresponding combinatorial results. The method we use relies primarily on the "magic extension" established recently…

We address the inverse problem of Lagrangian identification based on trajecto-ries in the context of nonlinear optimal control. We propose a general formulation of the inverse problem based on occupation measures and complementarity in…

In this paper, we extend recent results on the convergence of ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems, partially answering questions posed by the first author, Maass and the…

We study limit laws for return time processes defined on infinite conservative ergodic measure preserving dynamical systems. Especially for the critical cases with purely atomic limiting distribution we derive distorted processes posessing…

Recently, T. Tao gave a finitary proof a convergence theorem for multiple averages with several commuting transformations and soon later, T. Austin gave an ergodic proof of the same result. Although we give here one more proof of the same…

We study the occupation time statistics for non-Markovian random walkers based on the formalism of the generalized master equation for the Continuous-Time Random Walk. We also explore the case when the random walker additionally undergoes a…

We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…

Based on T.Tao's result of norm convergence of multiple ergodic averages for commut-ing transformation, we obtain there is a subsequence which converges almost everywhere. Meanwhile, the ergodic behaviour, which the time average is equal to…

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation…