Abstract: | For series of random variables $\sum\limits_{k = 1}^\infty {a_k x_k }$ ,a K ∈R 1, {X K } K=1 ∞ being an Ising system, i.e., for each n ≥ 2 the joint distribution of {X K } K=1 n has the form $$P_n (t_1 ,...,t_n ) = ch^{ - (n - 1)} J \cdot exp(J\sum\limits_{k - 1}^{n - 1} {t_k t_{k + 1} )\prod\limits_{k = 1}^n {\frac{1}{2}\delta (t_{k^{ - 1} }^2 ),J > 0} }$$ one obtains a criterion for almost everywhere convergence: $\sum\limits_{k = 1}^\infty {a_k^2< \infty }$ . The relation between the asymptotic behavior of large deviations of the sum and the rate of decrease of the sequence {ak} of the coefficients is investigated. |