The circular law for random band matrices: improved bandwidth for general models
| Autor: | Han, Yi |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider the convergence of ESD for non-Hermitian random band matrices with independent entries to the circular law, where the bandwidth scales like $n^\gamma$ and $n$ is the matrix size. We prove that the circular law limit holds provided that $\gamma>\frac{5}{6}$ for a very general class of inhomogeneous matrix models with Gaussian distribution and doubly stochastic variance profile, and provided that $\gamma>\frac{8}{9}$ if entries have symmetric subGaussian distribution. This improves previous works which essentially require $\gamma>\frac{32}{33}$. We also prove an extended form of product circular law with a growing number of matrices. Weak delocalization estimates on eigenvectors are also derived. The new technical input is new polynomial lower bounds on some intermediate small singular values. Comment: 19 pages |
| Databáze: | arXiv |
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