, Volume 209, Issue 3, pp 729-755

Bounds for Kac's Master Equation

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Abstract:

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/n 3. This and curvature information are used to bound the rate of convergence to stationarity.

Received: 26 April 1999 / Accepted: 30 August 1999