Mixing points on a circle

Authors:
Dana Randall;Peter Winkler
Affiliations:
College of Computing, Georgia Institute of Technology, Atlanta, GA;Dept. of Mathematics, Dartmouth College, Hanover, NH
Venue:
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Year:
2005

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Abstract

We determine, up to a log factor, the mixing time of a Markov chain whose state space consists of the successive distances between n labeled “dots” on a circle, in which one dot is selected uniformly at random and moved to a uniformly random point between its two neighbors. The method involves novel use of auxiliary discrete Markov chains to keep track of a vector of quadratic parameters.