article published yes Zhigang Bao author 442E6A6C-F248-11E8-B48F-1D18A9856A870000-0003-3036-1475 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Kevin Schnelli author 434AD0AE-F248-11E8-B48F-1D18A9856A870000-0003-0954-3231 LaEr department Random matrices, universality and disordered quantum systems project 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]. Springer Nature2020 eng 0021-7670 1565-8538 1804.11199 00061187940000810.1007/s11854-020-0135-2 142323-348 Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348. Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. 2020;142:323-348. doi:<a href="https://doi.org/10.1007/s11854-020-0135-2">10.1007/s11854-020-0135-2</a> Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” <i>Journal d’Analyse Mathematique</i>, vol. 142. Springer Nature, pp. 323–348, 2020. Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348. Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s11854-020-0135-2">https://doi.org/10.1007/s11854-020-0135-2</a>. Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>, vol. 142, Springer Nature, 2020, pp. 323–48, doi:<a href="https://doi.org/10.1007/s11854-020-0135-2">10.1007/s11854-020-0135-2</a>. Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. Springer Nature. <a href="https://doi.org/10.1007/s11854-020-0135-2">https://doi.org/10.1007/s11854-020-0135-2</a> 91042021-02-07T23:01:15Z2025-07-10T12:01:37Z