TY - JOUR
T1 - A Localization–Delocalization Transition for Nonhomogeneous Random Matrices
AU - Shou, Laura
AU - van Handel, Ramon
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/2
Y1 - 2024/2
N2 - We consider N×N self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with d nonzero entries per row. We show that such random matrices exhibit a canonical localization–delocalization transition near the edge of the spectrum: when d≫logN the random matrix possesses a delocalized approximate top eigenvector, while when d≪logN any approximate top eigenvector is localized. The key feature of this phenomenon is that it is universal with respect to the sparsity pattern, in contrast to the delocalization properties of exact eigenvectors which are sensitive to the specific sparsity pattern of the random matrix.
AB - We consider N×N self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with d nonzero entries per row. We show that such random matrices exhibit a canonical localization–delocalization transition near the edge of the spectrum: when d≫logN the random matrix possesses a delocalized approximate top eigenvector, while when d≪logN any approximate top eigenvector is localized. The key feature of this phenomenon is that it is universal with respect to the sparsity pattern, in contrast to the delocalization properties of exact eigenvectors which are sensitive to the specific sparsity pattern of the random matrix.
KW - 60B20
KW - Approximate eigenvectors
KW - Localization–delocalization transition
KW - Nonhomogeneous random matrices
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U2 - 10.1007/s10955-024-03234-7
DO - 10.1007/s10955-024-03234-7
M3 - Article
AN - SCOPUS:85185663515
SN - 0022-4715
VL - 191
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
M1 - 26
ER -