Asymptotically gaussian distribution for random perturbations of rotations of the circle

Let T _, be a transformation of the two-dimensional torus T ₂ given by the formula T _, (x, y)(2x, y+ +x) mod 1.A version of the functional central limit theorem is formulated for variables of the form ,where is an irrational number and f belongs to a class of real- valued functions on T ₂ described in terms of . The proof will be published elsewhere.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 78–81.This work was performed as part of the Russian-German project DFG-RFBR, grant 96-01-00096. The second author was also supported by the Russian Foundation for Basic Research, grant 96-01-00672.