SEMINAIRE MERCREDI 3 MARS 2004
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Edgardo Ugalde

Titre: Finite type approximations of Gibbs measures on sofic subshifts

Abstract: Consider a Hoder continuous potential \phi defined on the full shift
A^\nn, where A is a finite alphabet. Let X\subset A^\nn be a specified sofic
subshift. There is a natural nested sequence of subshifts of finite type (X_m)
converging to this sofic subshift. To this sequence we can associate a sequence of
Gibbs measures (\mu_\phi^m). We prove that this sequence weakly converges to a
Gibbs measure \mu_\phi at an exponential speed. Moreover, we show that this measure
is the unique equilibrium state of \phi and establish its \psi-mixing property,
implying weak Bernoullicity. We enphasize that our approach is contructive and
relies on the theory of primitive matrices.