Category: Physics

Summary: Estimating how finite-variance Student-t matrix entries shift the bandwidth where random band matrices cross from Wigner-Dyson to Poisson bulk spacing statistics.

Random band matrices are a standard model for localization and spectral crossover phenomena, but most threshold studies focus on Gaussian entries. This experiment asks where the bulk-spacing transition occurs when the matrix entries instead follow a finite-variance Student-t law, so rare but not infinite-variance couplings can reshape level statistics.

The script generates dense symmetric band matrices, measures bulk spacing ratios, and uses iterative deepening with bisection on the rescaled bandwidth parameter across system sizes from 64 to 2048. That turns the run into a direct estimate of the critical prefactor in the expected square-root bandwidth scaling.

The scientific value is comparative. Heavy-tailed random matrices and ordinary band-matrix transitions are both studied separately, but this experiment targets the finite-size crossover map for their combination in a single threshold calculation.

Method: Dense symmetric eigensolves with iterative deepening and bisection on the rescaled bandwidth in finite-variance Student-t random band matrices.

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