On the pseudocontinuation for random power series

We consider the boundary behavior of random power series. We show that such series do not admit pseudocontinuations across any arc of the circle of convergence almost surely. This generalizes classical results by Steinhaus, Paley, Zygmund, Ryll-Nardzewski on the a.s. absence of analytic continuation for random power series. As a corollary, we answer a question of N. Nikolski and D. Sarason by showing that a random function from the Hardy space is a.s. cyclic for the backward shift operator. The talk is based on joint work with Alexei Poltoratski.