Inhomogeneous random matrices have identical universal edge statistics if their variance-profile Markov chains satisfy short-to-long comparability, enabling analysis of band matrices, orbital models, and Hankel profiles in subcritical and critical regimes.
Delocalization of one-dimensional random band matrices.e-preprint
6 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.
Uniform single- and two-resolvent local laws for arbitrary deformations of Wigner matrices yield ETH and localization profiles for all λ and H0.
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.
Minimal support cardinality S_d(N) of nontrivial origin-nonzero Dirichlet solutions is nondecreasing in d, so S_4(N) ≳ N²/log N, matching even-dimensional constructions up to a log factor.
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.
citing papers explorer
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Edge Universality for Inhomogeneous Random Matrices II: Markov Chain Comparison and Critical Statistics
Inhomogeneous random matrices have identical universal edge statistics if their variance-profile Markov chains satisfy short-to-long comparability, enabling analysis of band matrices, orbital models, and Hankel profiles in subcritical and critical regimes.
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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.
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On a Rosenzweig-Porter-type model
Uniform single- and two-resolvent local laws for arbitrary deformations of Wigner matrices yield ETH and localization profiles for all λ and H0.
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Gradual eigenvector ergodization in coupled Ginibre matrices
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.
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On Support Cardinality for the Discrete Schr\"odinger Equation
Minimal support cardinality S_d(N) of nontrivial origin-nonzero Dirichlet solutions is nondecreasing in d, so S_4(N) ≳ N²/log N, matching even-dimensional constructions up to a log factor.
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Characteristic polynomials of non-Hermitian random band matrices near the threshold
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.