A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices.

Our main result is a local limit law tor the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law. Our approach is to adapt some techniques from recent papers of Erdös-Yau-Yin. We also use an algebraic description of the law of the anlicommutator of free semicircular variables due to Nica-Speicher, the lineatization trick due to Haagerup-Schultz-Thorbjørnsen in a self-adjointness-preserving variant and the Schwinger-Dyson equation. A by-product ot our work is a relatively simple deterministic version of the local semicircle law. [ABSTRACT FROM AUTHOR]