Year: 2026
Type: preprint
Abstract: 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, $p_{\rm nn}(S)\sim S^4$, 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.
Source: arXiv (Cornell University)
Authors: Basu, Pallab, Sarkar, Anurag
Institution: University of the Witwatersrand
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221554564