Communications in Mathematical Physics

, Volume 209, Issue 3, pp 729–755

Bounds for Kac's Master Equation

  • Persi Diaconis
  • Laurent Saloff-Coste

DOI: 10.1007/s002200050036

Cite this article as:
Diaconis, P. & Saloff-Coste, L. Comm Math Phys (2000) 209: 729. doi:10.1007/s002200050036


Mark Kac considered a Markov Chain on the n-sphere based on random rotations in randomly chosen coordinate planes. This same walk was used by Hastings on the orthogonal group. We show that the walk has spectral gap bounded below by c/n3. This and curvature information are used to bound the rate of convergence to stationarity.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Persi Diaconis
    • 1
  • Laurent Saloff-Coste
    • 2
  1. 1.Department of Mathematics, Stanford University, Stanford, CA 94305, USAUS
  2. 2.CNRS, Toulouse, FranceFR
  3. 3.Department of Mathematics, Cornell University, Ithaca, NY 14853, USA. E-mail: lsc@math.cornell.eduUS

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