Mixing Points on a Circle

  • Dana Randall
  • Peter Winkler
Conference paper

DOI: 10.1007/11538462_36

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3624)
Cite this paper as:
Randall D., Winkler P. (2005) Mixing Points on a Circle. In: Chekuri C., Jansen K., Rolim J.D.P., Trevisan L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dana Randall
    • 1
  • Peter Winkler
    • 2
  1. 1.College of ComputingGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Dept. of MathematicsDartmouth CollegeHanoverUSA

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