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

Ronen Eldan

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arXiv · 1106.0470

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

Ronen Eldan

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Abstract

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}. As a result, we attain a bound for the ?pi/2-covering time of a spherical brownian motion.

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Ronen Eldan. 2013-03-16. Extremal points of high dimensional random walks and mixing times of a Brownian motion on the sphere. https://arxiv.org/abs/1106.0470

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