Geodesic
Bounds on semigroups of random rotations on $SO(n)$
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 606-612

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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 $1/n^2$ and the entropy/entropy dissipation bound is bounded above by $n^3$.
Keywords: convergence to equilibrium, spectral gap. 
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     author = {E. Janvresse},
     title = {Bounds on semigroups of random rotations on $SO(n)$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {606--612},
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     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a15/}
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E. Janvresse. Bounds on semigroups of random rotations on $SO(n)$. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 606-612. http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a15/