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Generic properties of learning systems

Tomasz Szarek (2000)

Annales Polonici Mathematici

It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.

Gibbs measures in a markovian context and dimension

L. Farhane, G. Michon (2001)

Colloquium Mathematicae

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...

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