Category: Statistics

Summary: Testing whether heavy-tailed entries delay the breakdown of random matrix universality in sparse networks.

Random matrix theory predicts universal eigenvalue statistics (Tracy-Widom distribution at the edge) for dense Wigner matrices. When matrices become sparse (fewer nonzero entries), this universality breaks down at a critical sparsity. This experiment tests whether using heavy-tailed Student-t entries instead of Gaussian ones shifts that critical point.

The hypothesis is that heavy-tail resonances should delay the universality breakdown, meaning sparse heavy-tailed matrices maintain GOE-like edge statistics at lower densities than their Gaussian counterparts.

This GPU experiment performs large-scale eigenvalue decompositions on sparse symmetric matrices with Student-t entries, measuring edge spacing statistics across a range of sparsity levels to map the crossover.

Method: GPU dense eigensolve (cupy.linalg.eigvalsh) with iterative deepening based on GPU TFLOPS. Bisection on sparsity parameter.

What is measured: Edge spacing ratio, Tracy-Widom deviation, crossover sparsity exponent.