The origin of amplitude chaos and strings

We analytically study the peak statistics of an amplitude ensemble to identify the local mechanism responsible for peak repulsion. Our analytical approaches show that a smooth, nondegenerate ensemble of sufficiently differentiable amplitudes exhibits quartic nearest-neighbor repulsion, $p_{\mathrm{n}\mathrm{n}}(S)\sim S^4$, where $S$ is the spacing between adjacent peaks. We verify this prediction numerically for the tree-level highly excited string scattering amplitudes. Interestingly, we find the quartic repulsion to be robust by varying both the underlying ensemble and the amplitude functions, whereas a tunable cusp model shows that weakening differentiability changes the strength of the repulsion. Peak repulsion therefore defines a local universality class that is not unique to string theory and may occur in amplitude ensembles in other theories.