Y. Lacroix


Titre: "Local perturbations of energy and Kac's return time theorem"


Abstract: We use coupling technics and Kac's return time theorem to prove that if the energy is locally perturbated (not in the $\norm_\infty$ sense) then the $\bar{d}$-distance between equilibrium states remains small. Our basic example is that of ergodic $\Cal G$-functions (e.g. normalized energies) for the shift map on $\{0,1\}^{\Bbb N}$. From this some weak-$\star$ convergence may be obtained without $\norm_\infty\to 0$.

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