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We show how Rio's method [Probab. Theory Related Fields 104 (1996) 255--282]can be adapted to establish a rate of convergence in ${\frac{1}{\sqrt{n}}}$ inthe multidimensional central limit theorem for some stationary processes in thesense of the Kantorovich metric. We give two applications of this generalresult: in the case of the Knudsen gas and in the case of the Sinai billiard.

Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard