On Some Mean Matrix Inequalites of Dynamical Interest

@article{Rivin2003OnSM,
  title={On Some Mean Matrix Inequalites of Dynamical Interest},
  author={Igor Rivin},
  journal={Communications in Mathematical Physics},
  year={2003},
  volume={254},
  pages={651-658}
}
  • Igor Rivin
  • Published 2 December 2003
  • Mathematics
  • Communications in Mathematical Physics
AbstractLet A ∈ SL(n,ℝ). We show that for all n>2 there exist dimensional strictly positive constants Cn such that where ||A|| denotes the operator norm of A (which equals the largest singular value of A), ρ denotes the spectral radius, and the integral is with respect to the Haar measure on On, normalized to be a probability measure. The same result (with essentially the same proof) holds for the unitary group Un in place of the orthogonal group. The result does not hold in dimension 2… 
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