Colloquium de l'IDP
Powers of random matricesMichael Cowling (UNSW Sydney)
Thursday 20 June 2013 14:00 - Orléans - Amphithéâtre IRD
Résumé :
Suppose that $X$ is a uniformly distributed random element of the orthogonal group $\mathrm{O}(n)$. The powers $X^k$ are in general not uniformly distributed, but their distribution has been described by E. M. Rains. If $v$ is a unit vector in $\mathbb{R}^n$, then $X^k v$ is not uniformly distributed on the unit sphere either. We summarise what is known about this problem, and consider generalisations to unitary matrices and to more general compact Lie groups.
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