Category: Statistics

Summary: Measuring how heavy-tailed noise shifts the BBP transition for recovering a low-rank spike from a dense random matrix.

The BBP transition is the point where a planted low-rank signal separates from a random spectral background and becomes statistically recoverable. This experiment asks how that transition moves when the noise is not Gaussian but heavy tailed, using Student-t disorder where rare large entries can distort the spectrum.

The script generates dense symmetric matrices with a controllable spike strength and then carries a bisection bracket across increasing matrix sizes. By focusing on the threshold value rather than isolated sample plots, it produces a finite-size map of when spectral recovery appears in the heavy-tailed case.

That is scientifically useful because theory shows recovery can still occur, but the actual threshold value is not available in closed form for this regime. The computation therefore fills in the quantitative boundary numerically.

Method: Dense symmetric eigensolves with iterative deepening and bisection on spike strength in Student-t random matrices.

What is measured: Critical BBP threshold, finite-size crossover location, spectral separation diagnostics, and bracket width.