| Título: | The local semicircle law for a general class of random matrices |
| Autores: |
Erdős, László; LMU-University of Munich Knowles, Antti; New York University Yau, Horng-Tzer; Harvard University Yin, Jun; University of Wisconsin |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Random band matrix; local semicircle law; universality; eigenvalue rigidity 15B52; 82B44 |
| Descripción: | We consider a general class of $N\times N$ random matrices whose entries $h_{ij}$ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, $\max_{i,j} \mathbb{E} \left|h_{ij}\right|^2$. As a consequence, we prove the universality of the local $n$-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width $W\gg N^{1-\varepsilon_n}$ with some $\varepsilon_n>0$ and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments. |
| Idioma: | Inglés |
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