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Gibbs measures in a markovian context and dimension

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Farhane L., Michon G.

Colloquium Mathematicum

2001

tom 88

nr 2

215-223

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Farhane L.

1 Michon G.

1 2001

Wyniki wyszukiwania

Gibbs measures in a markovian context and dimension