Distribution Laws
GOE: Wigner surmise (β=1)
GUE: Wigner surmise (β=2)
Poisson: P(s)=e⁻ˢ
GSE (β=4)
Histogram (data)
GOE: P(s) = (π/2)s exp(−πs²/4)
GUE: P(s) = (32/π²)s² exp(−4s²/π)
Poisson: P(s) = e⁻ˢ
GSE: P(s) = (2¹⁸/3⁶π³)s⁴ exp(−64s²/9π)
Level repulsion: P(s)~sᵝ as s→0
β=1(GOE), 2(GUE), 4(GSE), 0(Poisson)