Extremal points of high dimensional random walks and mixing times of a Brownian motion on the sphere

Details Extremal points of high dimensional random walks and mixing times of a Brownian motion on the sphere Extremal points of high dimensional random walks and mixing times of a Brownian motion on the sphere

2011-06-02

arxiv.org/abs/1106.0470v2

Mathematics

Probability

14 Pages

Scientific paper

We derive asymptotics for the probability of the origin to be an extremal
point of a random walk in R^n. We show that in order for the probability to be
roughly 1/2, the number of steps of the random walk should be between e^{c n /
log n}$ and e^{C n log n}.

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