Wigner random banded matrices with sparse structure: Local spectral density of states

Random banded matrices with linearly increasing diagonal elements are recently considered as an attractive model for complex nuclei and atoms. Apart from early papers by Wigner there were no analytical studies on the subject. Ln this Letter we present analytical and numerical results for local spectral density of states (LDOS) for a more general case of matrices with a sparsity inside the band. The crossover from the semicircle form of LDOS to that given by the Breit-Wigner formula is studied in detail.