Almost-optimal bulk regularity conditions in the CLT for Wigner matrices
Abstract
We consider linear spectral statistics of the form tr ( (H)) for test functions of low regularity and Wigner matrices H with smooth entry distribution. We show that for functions in the Sobolev space H1/2+ or the space C1/2+, that are supported within the spectral bulk of the semicircle distribution, these linear spectral statistics have asymptotic Gaussian fluctuations with the same variance as in the CLT for functions of higher regularity, for any >0.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.