Discoveries / mathematical-physics

Spectral Edge of the Quartic SYK Model

Determine the leading asymptotic of the largest eigenvalue of the $N$-Majorana quartic SYK Hamiltonian as $N \to \infty$. The preprint proves $\lambda_1/\sqrt{N} \to 4\int_0^\infty g_0(t)^4\,dt \approx 0.32504$ almost surely, via the limiting free energy at every fixed positive temperature.