Category: Statistics

Summary: Testing whether a spike with both broad and local structure aligns with the leading sample eigenvector better than purely smooth or purely local spikes near the BBP crossover.

Spiked covariance models describe when a structured signal can be detected above random noise, but the geometry of that signal can matter as much as its strength. This experiment asks whether a mixed-support spike, combining a broad smooth component with a compact local block, is especially effective near the finite-sample BBP transition when the noise itself has intermediate block correlations.

The simulation compares smooth, local, and mixed spike geometries while varying the correlation structure of the noise bulk. The central observable is how strongly the leading sample eigenvector aligns with the planted spike, testing whether a multiscale signal can exploit mesoscale correlations without fully dissolving into the noise.

That makes the project a geometry-sensitive detection study rather than a standard phase-transition measurement. Its value is in asking whether multiscale structure can outperform simpler spike shapes in finite correlated samples.

Method: GPU batched finite-size sweeps of spiked covariance models with smooth, local, and mixed-support spikes under block-correlated noise.

What is measured: Leading-eigenvector alignment, localization crossover, dependence on spike geometry, and sensitivity to block-correlated noise.