K. Fukuyama & B. Petit


Titre: "Le théorème limite central pour les suites de Baker"


Résumé: Let $D=(\omega_n)_{n\ge0}$ be the multiplicative semi-group generated by the coprime integers $q_1,\dots q_\tau$ arranged in increasing order. If $f$ is a real-valued 1-periodic function, we consider the sums $S_nf(t)=\sum_{0\le k \le n-1} f(\omega_kt)$. For a large class of functions, we prove the existence of a limiting variance $\sigma^2$ for the sequence $\{S_nf/\sqrt n\}$, we give a function characterisation for the case when $\sigma=0$ and finally we prove a central limit theorem.

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