Category: Statistics

Summary: Mapping how heavy-tailed Student-t noise shifts the finite-size spike-detection threshold away from the Gaussian BBP benchmark.

In the classical BBP transition, a low-rank spike becomes detectable once its strength crosses a sharp threshold in Gaussian noise. This experiment asks how that transition shifts when the background noise is heavy-tailed, using Student-t disorder where analytic finite-size behavior is not known.

The code performs GPU-accelerated symmetric eigensolves while iteratively deepening matrix size and bisecting spike strength. It compares the estimated critical strength against the Gaussian reference value and tracks how the threshold bracket tightens under heavy-tailed fluctuations.

That makes the project a direct finite-size map of outlier emergence under non-Gaussian noise. The result is useful for understanding when a structured signal becomes spectrally visible once rare, large fluctuations dominate the background.

Method: GPU dense symmetric eigensolves with iterative deepening and bisection on spike strength beta for Student-t noise with fixed heavy-tail parameter.

What is measured: Critical spike threshold, matrix size, bracket width, heavy-tail parameter, eigensolve count, and comparison with the Gaussian BBP reference.