Provides uniform local laws and localization analysis for the general Rosenzweig-Porter model H = H0 + λW, generalizing previous results on deformed Wigner matrices.
Localization of one-dimensional random band matrices,arXiv:2508.05802v2 (2025)
4 Pith papers cite this work. Polarity classification is still indexing.
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The paper establishes rigorous lower bounds on eigenvector localization lengths for power-law random band matrices in four regimes of the decay exponent α, verifying a physical conjecture via new resolvent techniques.
Explicit large-N asymptotic formula for gradual eigenvector ergodization in two coupled Ginibre matrices, plus vanishing of eigenvalue density at the origin beyond critical scaled coupling |tilde c|=1.
The second correlation function of characteristic polynomials for non-Hermitian random band matrices is studied asymptotically in the critical regime W proportional to sqrt(N) as N and W tend to infinity.
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