Marc Raimondo - CMI

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Concentration for Riemannian manifolds Theorem (Ledoux, 1992) Assume: (1. manifold) (X,g) compact, connected, smooth Riemannian manifold, dimension ≥ 2 (2. volume) dµ normalized Riemannian volume element (3. Lipschitz) F 1−Lipschitz on X, i.e. |∇F | ≤ 1 (4. curvature) c(X) = inf{Ric(∇f, ∇f) : |∇f| = 1} Then µ{F ≥ � Ricci curvature Fdµ + t} ≤ e −ct2 /2 . Need to interpret (1) - (4) for F = σ1(U T X UY ) = R(X,Y ). Luminy 12/08 – p.34
Marc Raimondo The Talented Student Program: an integrated learning solution Hugh Miller and Marc Raimondo, School of Mathematics and Statistics Luminy 12/08 – p.35
Page 1 and 2: Marc Raimondo Luminy 12/08 - p.1
Page 3 and 4: The Annals of Statistics 2004, Vol.
Page 5 and 6: Effect of Ageing on Morphologic and
Page 7 and 8: Marc Raimondo Memorial Session: - N
Page 9 and 10: Theme � Many problems of classica
Page 11 and 12: Joint density of eigenvalues Single
Page 13 and 14: Symmetric Gaussian matrices A - sym
Page 15 and 16: f(x) 0.35 0.3 0.25 0.2 0.15 0.1 0.0
Page 17 and 18: I. Setting Outline 1. Single & Doub
Page 19 and 20: Second order accuracy For {real, co
Page 23 and 24: The Tracy-Widom approximation Let W
Page 25 and 26: Accuracy of approximate α th perce
Page 27 and 28: θ α log 10 n 1 0.5 p = 4 at 90th
Page 31 and 32: ‘Small’ vs. ‘Large’ Deviati
Page 33: Rmax as singular value Use SVD: X =
Page 37 and 38: Determinant representation: Correla
Page 39 and 40: After rescaling: Sτ(s,t) = 1 2 Uni
Page 41 and 42: Orthogonal Case - Convergence P { m
Page 43 and 44: Tail p−values: s = 2 variables F

Marc Raimondo - CMI

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