Category: Physics

Summary: Estimating how heavy-tailed matrix entries shift the bandwidth where random band matrices cross from Wigner-Dyson to Poisson spectral statistics.

Random band matrices are a standard model for localization, transport, and spectral crossover phenomena. This experiment asks how that crossover changes when the matrix entries are not Gaussian but instead come from a finite-variance heavy-tailed Student-t distribution, which can generate rare large couplings that reshape the spectrum.

The script generates symmetric random band matrices, measures spacing-ratio statistics, and uses GPU-accelerated iterative deepening with bisection on the rescaled bandwidth parameter. The target is the critical bandwidth prefactor where GOE-like level repulsion gives way to Poisson-like behavior.

That matters because heavy-tailed random matrices and Gaussian band matrices are both well studied, but their combination is less mapped in this finite-size threshold form. The experiment is designed to show whether rare resonances systematically delay the onset of the usual Wigner-to-Poisson transition.

Method: GPU dense symmetric eigensolve with iterative deepening and bisection on the rescaled bandwidth in heavy-tailed random band matrices.

What is measured: Critical bandwidth prefactor, spacing-ratio crossover, implied transition bandwidth, and bracket width.