Recurrence and transience of Rademacher series.

We introduce the notion of a-walk S(n) = a1X1 + ... + anXn, based on a sequence of positive numbers a = (a1; a2; ...) and a Rademacher sequence X1;X2; .... We study recurrence/transience (properly defined) of such walks for various sequences of a. In particular, we establish the classification in the cases where ak = [kβ], β > 0, as well as in the case ak = [logγ k] or ak = logγ k for > 1. [ABSTRACT FROM AUTHOR]