On the limit distributions and the asymptotics of extremal values for some sequences of random variables

The limit distributions are studied for some sequences of sums of coordinate random variables over the dynamical system, connected with the substitution of Rudin–Shapiro. The description of the limit distributions is presented on the basis of the expression for the sums of Rudin–Shapiro coefficients, obtained earlier. The expression of the density is given for the concrete subsequences and Markov representation for the “stationary” situation. The evalution of the excess is given for the wide class of substitutions. Bibliography: 11 titles.