Gibbs measures in a markovian context and dimension

L. Farhane, and G. Michon. "Gibbs measures in a markovian context and dimension." Colloquium Mathematicae 88.2 (2001): 215-223. <http://eudml.org/doc/283684>.

@article{L2001,
abstract = {The main goal is to use Gibbs measures in a markovian matrices context and in a more general context, to compute the Hausdorff dimension of subsets of [0, 1[ and [0, 1[². We introduce a parameter t which could be interpreted within thermodynamic framework as the variable conjugate to energy. In some particular cases we recover the Shannon-McMillan-Breiman and Eggleston theorems. Our proofs are deeply rooted in the properties of non-negative irreducible matrices and large deviations techniques as introduced by Ellis.},
author = {L. Farhane, G. Michon},
journal = {Colloquium Mathematicae},
keywords = {Gibbs measures; Markov matrices; Hausdorff dimension; large deviations},
language = {eng},
number = {2},
pages = {215-223},
title = {Gibbs measures in a markovian context and dimension},
url = {http://eudml.org/doc/283684},
volume = {88},
year = {2001},
}

TY - JOUR
AU - L. Farhane
AU - G. Michon
TI - Gibbs measures in a markovian context and dimension
JO - Colloquium Mathematicae
PY - 2001
VL - 88
IS - 2
SP - 215
EP - 223
AB - The main goal is to use Gibbs measures in a markovian matrices context and in a more general context, to compute the Hausdorff dimension of subsets of [0, 1[ and [0, 1[². We introduce a parameter t which could be interpreted within thermodynamic framework as the variable conjugate to energy. In some particular cases we recover the Shannon-McMillan-Breiman and Eggleston theorems. Our proofs are deeply rooted in the properties of non-negative irreducible matrices and large deviations techniques as introduced by Ellis.
LA - eng
KW - Gibbs measures; Markov matrices; Hausdorff dimension; large deviations
UR - http://eudml.org/doc/283684
ER -