Category: Physics

Summary: Mapping how heavy-tailed random matrices cross from Poisson-like to GOE-like level-spacing statistics as the tail exponent increases.

Random-matrix spacing statistics often distinguish localized from strongly mixed spectral behavior. This experiment studies heavy-tailed Levy matrices, asking how the average spacing ratio changes as the tail exponent alpha increases through the regime where rare large entries stop dominating the spectrum.

The script uses GPU eigenvalue decompositions at large matrix sizes to measure the spacing ratio across alpha and to test whether the crossover sharpens as system size grows. The goal is to locate not just a broad trend, but the finite-size transition structure itself.

That is useful because heavy-tailed ensembles can fall outside the most familiar universality classes. The result helps show how spectral statistics recover more standard random-matrix behavior as the tails become less extreme.

Method: GPU-based eigenvalue computations on large Levy random matrices, followed by finite-size analysis of spacing-ratio crossover versus tail exponent alpha.

What is measured: Mean spacing ratio, crossover location in alpha, crossover width versus system size, and comparison to Poisson and GOE benchmarks.