Marc Raimondo - CMI

Symmetric Gaussian matrices
A – symmetric N × N matrix drawn from (GOE)
f(A) = c exp{− 1
2 tr(AT A)}.
[for GUE: complex Hermitian]. Largest eigenvalue:
Centering and scaling constants:
θN = λmax(A)
µN = √ 2N, σN = 2 −1/2 N −1/6
Tracy-Widom limit: TW (1994, 1996) For β = 1, 2, 4 (R, C, Q),
θN − µN
σN
D
⇒ Fβ.
Luminy 12/08 – p.13