in this paper, a local approach to the concept of hudetz $g$-entropy is presented. the introduced concept is stated in terms of hudetz $g$-entropy. this representation is based on the concept of $g$-ergodic decomposition which is a result of the choquet's representation theorem for compact convex metrizable subsets of locally convex spaces.

S OF THE TALKS Hillel Furstenberg, Hebrew U. Qualitative Laws of Large Numbers. Abstract: If X1,X2, . . . ,Xn, . . . is an iid sequence of non-singular matrices, and we form the ”random product” Yn = X1 ∗ X2 ∗ X3 ∗ ⋯ ∗ Xn and let n → ∞ we find that the Yn tend to have a certain form. We analyze this phenomenon. If X1,X2, . . . ,Xn, . . . is an iid sequence of non-singular matrices, and we form ...

In this note we give a short proof of a pointwise ergodic theorem for measure preserving actions of word hyperbolic groups, also obtained recently by Bufetov, Khristoforov and Klimenko. Our approach also applies to infinite measure spaces and one application is to linear actions of discrete groups on the plane. 0. Introduction The well-known Birkhoff ergodic theorem for ergodic transformations ...

The probabilistic machinery (Central Limit Theorem, Feynman-Kac formula and Girsanov Theorem) is used to study the homogenization property for PDE with second-order partial differential operator in divergence-form whose coefficients are stationary, ergodic random fields. Furthermore, we use the theory of Dirichlet forms, so that the only conditions required on the coefficients are non degenerac...

This paper is the third part of our study started with Cattiaux, León and Prieur (2014 2013). For some ergodic hamiltonian systems we obtained a central limit theorem for a non-parametric estimator of the invariant density (Cattiaux et al. 2014) and of the drift term (Cattiaux et al. 2013), under partial observation (only the positions are observed). Here we obtain similarly a central limit the...

We characterize the points that satisfy Birkhoff’s ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space is not Martin-Löf random, there is a computable measure-preserving transformation and a computable set that witness that x is not typical with respect to the...