Category: Physics

Summary: Testing whether a rank-one spike supported on an intermediate-width corridor most strongly delocalizes the top eigenvector near the random-band localization threshold.

Random band matrices sit near a localization transition where eigenvectors can be sensitive to structured perturbations. This experiment asks how a fixed-norm rank-one spike changes the top eigenvector when that spike is supported not globally or at a point, but on a corridor of adjustable width.

The hypothesis is a support-size tradeoff. Very narrow spikes produce strongly localized outliers, while fully global spikes lose leverage against the near-localized band background. An intermediate-width corridor may therefore be the most effective way to delocalize the leading eigenvector near the transition.

That is a structured-perturbation question rather than a plain localization study. The value of the experiment is in mapping how geometry of the spike support reshapes spectral localization close to the band threshold.

Method: GPU-accelerated random-band-matrix simulations with a fixed-norm rank-one perturbation supported on corridors of varying width, measuring top-eigenvector localization near the band transition.

What is measured: Top-eigenvector localization or delocalization, dependence on corridor width, comparison with narrow and global spikes, and spectral crossover behavior near the band threshold.