F. Pène

Title: "Rate of convergence in the central limit theorem for the billiard tranformation."


Abstract : In this paper, we prove a rate of convergence in $n^{-{1\over 2}}$ in the central limit theorem in the case of the billiard transformation. For one-dimensional functions, we control the maximal decay between the distribution functions. For multi-dimensional functions, we control the Prokhorov metric. The result we get here for a generalised class of Hölder continuous functions is based on the construction of Young's tower.