Random power series near the endpoint of the convergence interval

Maga, Balazs and Maga, Péter (2018) Random power series near the endpoint of the convergence interval. PUBLICATIONES MATHEMATICAE DEBRECEN, 93 (3-4). pp. 413-424. ISSN 0033-3883

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Abstract

In this paper, we are going to consider power series Sigma(infinity)(n=1)a(n)x(n), where the coefficients a(n) are chosen independently at random from a finite set with uniform distribution. We prove that if the expected value of the coefficients is 0, then lim sup(x -> 1-)Sigma(infinity)(n=1)a(n)x(n) = infinity, lim inf(x -> 1-)Sigma(infinity)(n=1)a(n)x(n) = -infinity, with probability 1. We investigate the analogous question in terms of Baire categories.

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