Category: Physics

Summary: Testing how finite-variance heavy-tailed entries shift the sparsity level where sparse Wigner matrices lose GOE-like edge universality.

Sparse random matrices can leave the universal GOE edge-statistics regime when the graph becomes too dilute, but heavy-tailed entries may change where that breakdown occurs. This experiment asks whether finite-variance Student-t matrix elements delay the loss of Tracy-Widom-like edge behavior compared with the better-studied Gaussian sparse-Wigner case.

The script performs GPU finite-size sweeps and threshold mapping for symmetric sparse Wigner matrices with heavy-tailed entries. It targets the critical sparsity exponent where edge universality fails, treating rare but finite-variance resonances as a possible mechanism that shifts the crossover.

That makes the project a combined sparsity-and-tail study rather than an ordinary universality check. The value is in directly mapping the finite-size boundary between GOE-like behavior and its breakdown in a regime that appears less charted than either sparse Gaussian or dense heavy-tailed ensembles alone.

Method: GPU finite-size threshold sweeps for sparse symmetric Wigner matrices with Student-t entries, focused on edge-statistics crossover behavior.

What is measured: Critical sparsity exponent, edge-universality crossover, finite-size drift, and comparisons with Gaussian sparse-Wigner behavior.