Bounds for Kac ’ S Master Equation

  title={Bounds for Kac ’ S Master Equation},
  author={Persi Diaconis},
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. Research partially supported by Nato Grant CRG 950686 and by NSF Grants DMS-9802855 and DMS-9504379 Typeset by AMS-TEX 1 2 PERSI DIACONIS AND LAURENT SALOFF–COSTE 
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