TY - JOUR AB - We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5]. AU - Bao, Zhigang AU - Erdös, László AU - Schnelli, Kevin ID - 9104 JF - Journal d'Analyse Mathematique SN - 00217670 TI - On the support of the free additive convolution VL - 142 ER -