This article is cited in 2 papers

Short Communications

Bounds on semigroups of random rotations on $SO(n)$

E. Janvresse

Université de Rouen

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 $1/n^2$ and the entropy/entropy dissipation bound is bounded above by $n^3$.

Keywords: convergence to equilibrium, spectral gap.

Received: 13.12.2001

Language: English

DOI: 10.4213/tvp3701

 English version: Theory of Probability and its Applications, 2003, 47:3, 526–532

Bibliographic databases:

• 
• 
•