Asymptotic Shannon entropy on G/H equals the spectral radius c(G,H;μ) for finite-entropy measures, with Rényi rates converging and explicit classifications for subgroups having pair rapid decay or subexponential Lorentz control, including equivalence to finite index in SL_n(Z) for n≥3.
An example of a non-nuclear C*-algebra, which has the metric approximation prop- erty.Inventiones Mathematicae, 50(3):279–293
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Entropy on Homogeneous Spaces and Classification Results for Subgroups with the Pair Rapid Decay Property
Asymptotic Shannon entropy on G/H equals the spectral radius c(G,H;μ) for finite-entropy measures, with Rényi rates converging and explicit classifications for subgroups having pair rapid decay or subexponential Lorentz control, including equivalence to finite index in SL_n(Z) for n≥3.