%0 Journal Article
%T Regularity of Polynomials in Free Variables
%A I. Charlesworth
%A D. Shlyakhtenko
%J Mathematics
%D 2014
%I arXiv
%X We show that the spectral measure of any non-commutative polynomial of a non-commutative $n$-tuple cannot have atoms if the free entropy dimension of that $n$-tuple is $n$ (see also work of Mai, Speicher, and Weber). Under stronger assumptions on the $n$-tuple, we prove that the spectral measure is not singular, and measures of intervals surrounding any point may not decay slower than polynomially as a function of the interval's length.
%U http://arxiv.org/abs/1408.0580v2