A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices
نویسنده
چکیده
Our main result is a local limit law for 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 one of the recent papers of Erdös-Yau-Yin. We also use an algebraic description of the law of the anticommutator of free semicircular variables due to Nica-Speicher, a self-adjointness-preserving variant of the linearization trick due to HaagerupSchultz-Thorbjørnsen and the Schwinger-Dyson equation. A byproduct of our work is a relatively simple deterministic version of the local semicircle law.
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تاریخ انتشار 2013