{"date_updated":"2021-01-12T06:50:42Z","language":[{"iso":"eng"}],"abstract":[{"text":"We prove that the system of subordination equations, defining the free additive convolution of two probability measures, is stable away from the edges of the support and blow-up singularities by showing that the recent smoothness condition of Kargin is always satisfied. As an application, we consider the local spectral statistics of the random matrix ensemble A+UBU⁎A+UBU⁎, where U is a Haar distributed random unitary or orthogonal matrix, and A and B   are deterministic matrices. In the bulk regime, we prove that the empirical spectral distribution of A+UBU⁎A+UBU⁎ concentrates around the free additive convolution of the spectral distributions of A and B   on scales down to N−2/3N−2/3.","lang":"eng"}],"doi":"10.1016/j.jfa.2016.04.006","_id":"1434","department":[{"_id":"LaEr"}],"author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","first_name":"Kevin"}],"scopus_import":1,"intvolume":"       271","publisher":"Academic Press","status":"public","citation":{"mla":"Bao, Zhigang, et al. “Local Stability of the Free Additive Convolution.” <i>Journal of Functional Analysis</i>, vol. 271, no. 3, Academic Press, 2016, pp. 672–719, doi:<a href=\"https://doi.org/10.1016/j.jfa.2016.04.006\">10.1016/j.jfa.2016.04.006</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,” <i>Journal of Functional Analysis</i>, vol. 271, no. 3. Academic Press, pp. 672–719, 2016.","ista":"Bao Z, Erdös L, Schnelli K. 2016. Local stability of the free additive convolution. Journal of Functional Analysis. 271(3), 672–719.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2016). Local stability of the free additive convolution. <i>Journal of Functional Analysis</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jfa.2016.04.006\">https://doi.org/10.1016/j.jfa.2016.04.006</a>","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Stability of the Free Additive Convolution.” <i>Journal of Functional Analysis</i>. Academic Press, 2016. <a href=\"https://doi.org/10.1016/j.jfa.2016.04.006\">https://doi.org/10.1016/j.jfa.2016.04.006</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016) 672–719.","ama":"Bao Z, Erdös L, Schnelli K. Local stability of the free additive convolution. <i>Journal of Functional Analysis</i>. 2016;271(3):672-719. doi:<a href=\"https://doi.org/10.1016/j.jfa.2016.04.006\">10.1016/j.jfa.2016.04.006</a>"},"publication":"Journal of Functional Analysis","date_created":"2018-12-11T11:52:00Z","publication_status":"published","year":"2016","oa":1,"quality_controlled":"1","ec_funded":1,"day":"01","volume":271,"oa_version":"Preprint","page":"672 - 719","title":"Local stability of the free additive convolution","publist_id":"5764","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","issue":"3","month":"08","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","date_published":"2016-08-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.05905"}]}