Category: Physics

Summary: Estimating when a minority central spectral miniband detaches between two heavy-tailed outer shoulders in a deformed random-matrix model.

Heavy-tailed random matrices can produce rare large entries that reshape spectral bands in ways not seen in Gaussian models. This experiment asks when a small neutral subpopulation remains visible as a distinct central miniband instead of being swallowed by the broader heavy-tailed bulk.

The script studies a deformed Wigner-style addition problem with Student-t disorder, a fixed minority center fraction, and GPU-accelerated iterative deepening. It bisects the deformation strength until the center cluster satisfies gap-ratio and occupancy criteria consistent with a detached miniband between two outer shoulders.

That is a specific finite-size spectral-geometry question rather than a generic heavy-tail benchmark. The value is in mapping the detachment threshold directly, which is less charted than broad questions about whether heavy tails merely widen or distort the bulk.

Method: GPU random-matrix simulations with iterative deepening and bisection on deformation strength, using spectral gap-ratio criteria to detect miniband detachment.

What is measured: Critical deformation threshold, gap ratio, center-band occupancy, mean gap ratio, and bracket width.