Hit-and-run from a corner

Authors:
László Lovász;Santosh Vempala
Affiliations:
Microsoft Research, Redmond, WA;Massachusetts Institute of Technology, Cambridge, MA
Venue:
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Year:
2004

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Abstract

We show that the hit-and-run random walk mixes rapidly starting from any interior point of a convex body. This is the first random walk known to have this property. In contrast, the ball walk can take exponentially many steps from some starting points.