Marc Raimondo - CMI

Wishart: Concentration for l1
A ∼ Wp(n,I), A = X T X X ∼ N(0,In ⊗ Ip)
Theorem (e.g. Davidson-Szarek, 2001) With l1(A) = σ 2 1(X),
and
P {σ1(X) > Eσ1(X) + √ nt} ≤ e −nt2 /2 ,
Eσ1(X) ≤ √ n + √ p.
from Standard Result: If X ∼ Nm(0,I) and f : R m → R is
Lipschitz-1 (implied by |∇f| ≤ 1), then
P {f(X) > Ef(X) + s} ≤ e −s2 /2 .
Luminy 12/08 – p.30