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.
Localization of one-dimensional random band matrices,arXiv:2508.05802v2 (2025)
3 Pith papers cite this work. Polarity classification is still indexing.
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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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Localization Lengths of Power-Law Random Band Matrices
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.