Abstract
In order to generate random orthogonal matrices, Hastings [Biometrika, 57 (1970), pp. 97--109] considered a Markov chain on the orthogonal group SO(n) generated by random rotations on randomly selected coordinate planes. We investigate different ways to measure the convergence to equilibrium of this walk. To this end, we prove, up to a multiplicative constant, that the spectral gap of this walk is bounded below by 1/n2 and the entropy/entropy dissipation bound is bounded above by n3 .
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