{"date_created":"2018-12-11T11:48:13Z","abstract":[{"lang":"eng","text":"Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + UBU∗ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate in the bulk of the spectrum."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"publication_status":"published","oa":1,"acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation","year":"2017","title":"Convergence rate for spectral distribution of addition of random matrices","month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.03076"}],"scopus_import":1,"publication":"Advances in Mathematics","status":"public","intvolume":" 319","day":"15","quality_controlled":"1","oa_version":"Submitted Version","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","first_name":"Zhigang"},{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","first_name":"Kevin"}],"publisher":"Academic Press","citation":{"apa":"Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. *Advances in Mathematics*. Academic Press. https://doi.org/10.1016/j.aim.2017.08.028","short":"Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” *Advances in Mathematics*. Academic Press, 2017. https://doi.org/10.1016/j.aim.2017.08.028.","ama":"Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices. *Advances in Mathematics*. 2017;319:251-291. doi:10.1016/j.aim.2017.08.028","mla":"Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” *Advances in Mathematics*, vol. 319, Academic Press, 2017, pp. 251–91, doi:10.1016/j.aim.2017.08.028.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” *Advances in Mathematics*, vol. 319. Academic Press, pp. 251–291, 2017."},"language":[{"iso":"eng"}],"ec_funded":1,"volume":319,"type":"journal_article","doi":"10.1016/j.aim.2017.08.028","date_published":"2017-10-15T00:00:00Z","date_updated":"2021-01-12T08:13:07Z","department":[{"_id":"LaEr"}],"_id":"733","page":"251 - 291","publist_id":"6935"}