Universality of the Local Regime for the Block Band Matrices with a Finite Number of Blocks

作者：Shcherbina Tatyana^*

来源：Journal of Statistical Physics, 2014, 155(3): 466-499.

DOI：10.1007/s10955-014-0964-4

• Random matrices
• Wegner model
• Band matrices
• Universality

We consider the block band matrices, i.e. the Hermitian matrices , with elements , where (they parameterize the lattice sites) and (they parameterize the orbitals on each site). The entries are random Gaussian variables with mean zero such that where , . This matrices are the special case of Wegner%26apos;s -orbital models. Assuming that the number of sites is finite, we prove universality of the local eigenvalue statistics of for the energies vertical bar lambda(0)vertical bar %26lt; root 2.

• 出版日期2014-5