Recurrence of the twisted planar random walk

Details Recurrence of the twisted planar random walk Recurrence of the twisted planar random walk

2008-03-05

arxiv.org/abs/0803.0724v1

Mathematics

Dynamical Systems

11 pages

Scientific paper

We show that the "twisted" planar random walk - which results by summing up stationary increments rotated by multiples of a fixed angle - is recurrent under diverse assumptions on the increment process. For example, if the increment process is alpha-mixing and of finite second moment, then the twisted random walk is recurrent for every angle fixed choice of the angle out of a set of full Lebesgue measure, no matter how slow the mixing coefficients decay.

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