Unique Bernoulli g-measures

REGULARITY CONDITIONS AND BERNOULLI PROPERTIES OF EQUILIBRIUM STATES AND g-MEASURES

When T :X −→X is a one-sided topologically mixing subshift of finite type and φ :X −→R is a continuous function, one can define the Ruelle operator Lφ :C(X)−→C(X) on the space C(X) of real-valued continuous functions on X. The dual operator Lφ always has a probability measure ν as an eigenvector corresponding to a positive eigenvalue (Lφν=λν with λ> 0). Necessary and sufficient conditions on su...

Image Measures of Infinite Product Measures and Generalized Bernoulli Convolutions

We examine measure preserving mappings f acting from a probability space (Ω, F, μ) into a probability space (Ω, F , μ) , where μ = μ(f−1). Conditions on f , under which f preserves the relations ”to be singular” and ”to be absolutely continuous” between measures defined on (Ω, F ) and corresponding image measures, are investigated. We apply the results to investigate the distribution of the ran...

Homeomorphic Bernoulli Trial Measures and Ergodic Theory

We survey the some of the main results, ideas and conjectures concerning two problems and their connections. The first problem concerns determining when two Bernoulli trial measures are homeomorphic to each other, i.e. when one is the image measure of the other via a homeomorphism of the Cantor space. The second problem concerns the following. Given a positive integer k characterize those Berno...

p-Adic Measures and Bernoulli Numbers

Poincaré inequalities for inhomogeneous Bernoulli measures

Recently there has been a lot of interest in the transport properties of particle systems in random media [AHL, BE, F, GP, KPW, K, MA, R, Se]. A simple model for which the hydrodynamic scaling limit can be obtained is the Kawasaki dynamics for random Bernoulli measures [Q], [QY]. Such systems have been used to model electron transport in doped crystals. The hydrodynamic limit is a nonlinear dif...