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

Eldan, Ronen. "Extremal points of high-dimensional random walks and mixing times of a brownian motion on the sphere." Annales de l'I.H.P. Probabilités et statistiques 50.1 (2014): 95-110. <http://eudml.org/doc/272060>.

@article{Eldan2014,
abstract = {We derive asymptotics for the probability that the origin is an extremal point of a random walk in $\mathbb \{R\}^\{n\}$. We show that in order for the probability to be roughly $1/2$, the number of steps of the random walk should be between $\mathrm \{e\}^\{n/(C\log n)\}$ and $\mathrm \{e\}^\{Cn\log n\}$ for some constant $C&gt;0$. As a result, we attain a bound for the $\frac\{\pi \}\{2\}$-covering time of a spherical Brownian motion.},
author = {Eldan, Ronen},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random walk; convex hull; mixing time; spherical coverings; extreme point},
language = {eng},
number = {1},
pages = {95-110},
publisher = {Gauthier-Villars},
title = {Extremal points of high-dimensional random walks and mixing times of a brownian motion on the sphere},
url = {http://eudml.org/doc/272060},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Eldan, Ronen
TI - Extremal points of high-dimensional random walks and mixing times of a brownian motion on the sphere
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 1
SP - 95
EP - 110
AB - We derive asymptotics for the probability that the origin is an extremal point of a random walk in $\mathbb {R}^{n}$. We show that in order for the probability to be roughly $1/2$, the number of steps of the random walk should be between $\mathrm {e}^{n/(C\log n)}$ and $\mathrm {e}^{Cn\log n}$ for some constant $C&gt;0$. As a result, we attain a bound for the $\frac{\pi }{2}$-covering time of a spherical Brownian motion.
LA - eng
KW - random walk; convex hull; mixing time; spherical coverings; extreme point
UR - http://eudml.org/doc/272060
ER -