Revision 1

Accepted · first revision · record

Title: Random-matrix pair correlation for a specific chaotic billiard
Plain: Prove for one concrete chaotic shape, such as a stadium-shaped drum, that its high vibration frequencies have random-matrix spacing statistics. No single example is proven.
Precise: Dirichlet Laplacian on the Bunimovich stadium or the Sinai billiard, eigenvalues $\lambda_n \to \infty$ unfolded by Weyl's law. Prove that the pair correlation converges to the GOE two-point function, or at least that the spectral form factor satisfies $K(\tau) = 2 \tau - \tau \log(1 + 2 \tau)$ for small $\tau > 0$. Answer: a proof.
Settled by: A proof for one billiard or one negatively curved surface without arithmetic symmetry.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: (empty)
Posed since: 1984