Quantization dimension for Gibbs-like measures on cookie-cutter sets
نویسندگان
چکیده
منابع مشابه
Optimal quantization for uniform distributions on Cantor-like sets
In this paper, the problem of optimal quantization is solved for uniform distributions on some higher dimensional, not necessarily self-similar N−adic Cantor-like sets. The optimal codebooks are determined and the optimal quantization error is calculated. The existence of the quantization dimension is characterized and it is shown that the quantization coefficient does not exist. The special ca...
متن کاملRemarks on Gibbs Measures for Fibred Systems
1. Gibbs measures for bred systems In 4] we investigated the existence and uniqueness of a system of conditional measures for bred systems which plays a similar role as conformal measures for non-bred one-dimensional dynamical systems. In this note we add some general properties and make some additional remarks about this concept. Recall that a bred system Y = (Y; T; X; S;) consists of two dyna...
متن کاملGibbs measures on Brownian currents
Motivated by applications to quantum field theory we consider Gibbs measures for which the reference measure is Wiener measure and the interaction is given by a double stochastic integral and a pinning external potential. In order properly to characterize these measures through DLR equations, we are led to lift Wiener measure and other objects to a space of configurations where the basic observ...
متن کاملGibbs Measures on Brownian Paths
This is a summary of results based upon 1, 4] outlining how Gibbs measures can be deened on Brownian paths and what are their most important properties. Such Gibbs measures have a number of applications in Euclidean quantum eld theory, statistical mechanics, stochastic (partial) diierential equations and other areas.
متن کاملSpectral Triples and Gibbs Measures for Expanding Maps on Cantor Sets
Let T : Λ → Λ be an expanding map on a Cantor set. For each suitably normalized Hölder continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as a noncommutative measure.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 2014
ISSN: 2156-2261
DOI: 10.1215/21562261-2642377