Wigner–Dyson vs. Poisson level spacing distributions in random matrices
The BGS conjecture (Bohigas–Giannoni–Schmit, 1984) states that quantum systems whose classical limit is chaotic have level spacings following the Wigner–Dyson distribution from Random Matrix Theory. Integrable systems follow Poisson statistics (uncorrelated levels). The GOE Wigner surmise: P(s) = (π/2)s·exp(−πs²/4); GUE: P(s) = (32/π²)s²·exp(−4s²/π).