Category: Statistics

Summary: Finding when a minority component in an asymmetrically deformed heavy-tailed random matrix detaches into its own resolved spectral island.

Random-matrix spectra can split into separated bands when a structured deformation is strong enough, but the onset of that split is less understood when the noise is heavy-tailed and the two deformed populations are unequal. This experiment asks when the minority species in a Student-t Wigner matrix plus an unequal two-atom diagonal deformation peels away from the bulk and forms a distinct spectral island.

The code performs GPU-accelerated dense eigensolves while iteratively deepening system size and bisecting the deformation parameter. It measures the emerging band gap, the detached minority fraction, and how accurately the isolated island aligns with the intended minority sector.

That makes the project a finite-size threshold study of asymmetric spectral separation under heavy-tailed disorder. The result is useful for understanding when structured minorities become spectrally visible rather than remaining absorbed into a noisy bulk.

Method: GPU dense symmetric eigensolves with iterative deepening and bisection on deformation strength delta in a heavy-tailed free-addition ensemble.

What is measured: Critical deformation threshold, gap ratio, detached minority fraction, minority alignment error, matrix size, and bracket width.