[{"month":"05","arxiv":1,"department":[{"_id":"LaEr"}],"article_number":"e44","file":[{"access_level":"open_access","content_type":"application/pdf","success":1,"file_name":"2021_ForumMath_Bao.pdf","checksum":"47c986578de132200d41e6d391905519","relation":"main_file","creator":"cziletti","date_updated":"2021-06-15T14:40:45Z","file_size":483458,"date_created":"2021-06-15T14:40:45Z","file_id":"9555"}],"oa":1,"language":[{"iso":"eng"}],"citation":{"ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021.","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2021). Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"27","scopus_import":"1","author":[{"first_name":"Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","first_name":"Kevin","orcid":"0000-0003-0954-3231"}],"oa_version":"Published Version","title":"Equipartition principle for Wigner matrices","volume":9,"date_created":"2021-06-13T22:01:33Z","article_type":"original","has_accepted_license":"1","abstract":[{"text":"We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. ","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"         9","file_date_updated":"2021-06-15T14:40:45Z","publication_status":"published","publication_identifier":{"eissn":["20505094"]},"isi":1,"year":"2021","external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"status":"public","publication":"Forum of Mathematics, Sigma","project":[{"call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"date_published":"2021-05-27T00:00:00Z","acknowledgement":"The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","article_processing_charge":"No","doi":"10.1017/fms.2021.38","publisher":"Cambridge University Press","_id":"9550","date_updated":"2023-08-08T14:03:40Z","type":"journal_article","ddc":["510"],"quality_controlled":"1"},{"publisher":"Elsevier","article_processing_charge":"No","doi":"10.1016/j.jfa.2020.108639","type":"journal_article","_id":"10862","date_updated":"2023-08-24T14:08:42Z","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1708.01597","open_access":"1"}],"external_id":{"isi":["000559623200009"],"arxiv":["1708.01597"]},"isi":1,"year":"2020","keyword":["Analysis"],"status":"public","publication":"Journal of Functional Analysis","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"date_published":"2020-10-15T00:00:00Z","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","ec_funded":1,"title":"Spectral rigidity for addition of random matrices at the regular edge","oa_version":"Preprint","day":"15","scopus_import":"1","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"date_created":"2022-03-18T10:18:59Z","article_type":"original","volume":279,"abstract":[{"lang":"eng","text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix."}],"intvolume":"       279","publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"arxiv":1,"month":"10","article_number":"108639","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>.","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279, no. 7. Elsevier, 2020.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020)."},"issue":"7"},{"main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"quality_controlled":"1","page":"323-348","_id":"9104","date_updated":"2023-08-24T11:16:03Z","type":"journal_article","article_processing_charge":"No","doi":"10.1007/s11854-020-0135-2","publisher":"Springer Nature","ec_funded":1,"acknowledgement":"Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195.","date_published":"2020-11-01T00:00:00Z","publication":"Journal d'Analyse Mathematique","status":"public","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"year":"2020","isi":1,"external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"publication_status":"published","publication_identifier":{"issn":["00217670"],"eissn":["15658538"]},"intvolume":"       142","abstract":[{"text":"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].","lang":"eng"}],"volume":142,"date_created":"2021-02-07T23:01:15Z","article_type":"original","scopus_import":"1","day":"01","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","last_name":"Bao"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László"},{"last_name":"Schnelli","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin"}],"title":"On the support of the free additive convolution","oa_version":"Preprint","citation":{"chicago":"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>.","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","apa":"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>","mla":"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>.","ama":"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>","ieee":"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.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"month":"11","arxiv":1},{"year":"2019","isi":1,"external_id":{"isi":["000466616100003"],"arxiv":["1612.05920"]},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"status":"public","publication":"Annals of Probability","ec_funded":1,"date_published":"2019-05-01T00:00:00Z","doi":"10.1214/18-AOP1284","article_processing_charge":"No","publisher":"Institute of Mathematical Statistics","date_updated":"2023-08-28T09:32:29Z","_id":"6511","type":"journal_article","page":"1270-1334","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.05920"}],"quality_controlled":"1","arxiv":1,"month":"05","department":[{"_id":"LaEr"}],"oa":1,"language":[{"iso":"eng"}],"issue":"3","citation":{"ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. <i>Annals of Probability</i>. 2019;47(3):1270-1334. doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” <i>Annals of Probability</i>, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2019). Local single ring theorem on optimal scale. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>","mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","first_name":"Kevin","orcid":"0000-0003-0954-3231"}],"day":"01","scopus_import":"1","oa_version":"Preprint","title":"Local single ring theorem on optimal scale","volume":47,"date_created":"2019-06-02T21:59:13Z","abstract":[{"text":"Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N).","lang":"eng"}],"intvolume":"        47","publication_identifier":{"issn":["00911798"]},"publication_status":"published"},{"citation":{"ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” <i>Advances in Mathematics</i>, vol. 319. Academic Press, pp. 251–291, 2017.","short":"Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.","ama":"Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices. <i>Advances in Mathematics</i>. 2017;319:251-291. doi:<a href=\"https://doi.org/10.1016/j.aim.2017.08.028\">10.1016/j.aim.2017.08.028</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. <i>Advances in Mathematics</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.aim.2017.08.028\">https://doi.org/10.1016/j.aim.2017.08.028</a>","mla":"Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” <i>Advances in Mathematics</i>, vol. 319, Academic Press, 2017, pp. 251–91, doi:<a href=\"https://doi.org/10.1016/j.aim.2017.08.028\">10.1016/j.aim.2017.08.028</a>.","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.” <i>Advances in Mathematics</i>. Academic Press, 2017. <a href=\"https://doi.org/10.1016/j.aim.2017.08.028\">https://doi.org/10.1016/j.aim.2017.08.028</a>."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"month":"10","publication_status":"published","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."}],"intvolume":"       319","volume":319,"date_created":"2018-12-11T11:48:13Z","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231"}],"scopus_import":"1","day":"15","oa_version":"Submitted Version","title":"Convergence rate for spectral distribution of addition of random matrices","ec_funded":1,"date_published":"2017-10-15T00:00:00Z","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"status":"public","publication":"Advances in Mathematics","publist_id":"6935","isi":1,"year":"2017","external_id":{"isi":["000412150400010"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.03076"}],"quality_controlled":"1","page":"251 - 291","date_updated":"2023-09-28T11:30:42Z","_id":"733","type":"journal_article","doi":"10.1016/j.aim.2017.08.028","article_processing_charge":"No","publisher":"Academic Press"},{"quality_controlled":"1","ddc":["530"],"page":"673 - 776","type":"journal_article","_id":"1528","date_updated":"2023-09-20T09:42:12Z","publisher":"Springer","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00440-015-0692-y","date_published":"2017-04-01T00:00:00Z","acknowledgement":"Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L. Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to the anonymous referees for careful reading and valuable comments, which helped to improve the organization.","ec_funded":1,"publication":"Probability Theory and Related Fields","status":"public","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"publist_id":"5644","external_id":{"isi":["000398842700004"]},"isi":1,"year":"2017","file_date_updated":"2020-07-14T12:45:00Z","publication_status":"published","publication_identifier":{"issn":["01788051"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"       167","abstract":[{"text":"We consider N×N Hermitian random matrices H consisting of blocks of size M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized.","lang":"eng"}],"has_accepted_license":"1","date_created":"2018-12-11T11:52:32Z","article_type":"original","volume":167,"oa_version":"Published Version","title":"Delocalization for a class of random block band matrices","scopus_import":"1","day":"01","author":[{"last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","first_name":"Zhigang"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Bao Z, Erdös L. Delocalization for a class of random block band matrices. <i>Probability Theory and Related Fields</i>. 2017;167(3-4):673-776. doi:<a href=\"https://doi.org/10.1007/s00440-015-0692-y\">10.1007/s00440-015-0692-y</a>","ieee":"Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” <i>Probability Theory and Related Fields</i>, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.","short":"Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.","chicago":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” <i>Probability Theory and Related Fields</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00440-015-0692-y\">https://doi.org/10.1007/s00440-015-0692-y</a>.","ista":"Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 167(3–4), 673–776.","apa":"Bao, Z., &#38; Erdös, L. (2017). Delocalization for a class of random block band matrices. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-015-0692-y\">https://doi.org/10.1007/s00440-015-0692-y</a>","mla":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” <i>Probability Theory and Related Fields</i>, vol. 167, no. 3–4, Springer, 2017, pp. 673–776, doi:<a href=\"https://doi.org/10.1007/s00440-015-0692-y\">10.1007/s00440-015-0692-y</a>."},"issue":"3-4","pubrep_id":"489","language":[{"iso":"eng"}],"oa":1,"file":[{"creator":"system","date_updated":"2020-07-14T12:45:00Z","date_created":"2018-12-12T10:08:05Z","file_size":1615755,"file_id":"4665","content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-489-v1+1_s00440-015-0692-y.pdf","checksum":"67afa85ff1e220cbc1f9f477a828513c","relation":"main_file"}],"department":[{"_id":"LaEr"}],"month":"04"},{"has_accepted_license":"1","intvolume":"       349","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix."}],"file_date_updated":"2020-07-14T12:44:39Z","publication_status":"published","publication_identifier":{"issn":["00103616"]},"day":"01","scopus_import":"1","author":[{"full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","orcid":"0000-0003-3036-1475","first_name":"Zhigang"},{"last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László"},{"orcid":"0000-0003-0954-3231","first_name":"Kevin","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli"}],"oa_version":"Published Version","title":"Local law of addition of random matrices on optimal scale","volume":349,"date_created":"2018-12-11T11:50:43Z","oa":1,"language":[{"iso":"eng"}],"pubrep_id":"722","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00220-016-2805-6\">https://doi.org/10.1007/s00220-016-2805-6</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-016-2805-6\">https://doi.org/10.1007/s00220-016-2805-6</a>","mla":"Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>, vol. 349, no. 3, Springer, 2017, pp. 947–90, doi:<a href=\"https://doi.org/10.1007/s00220-016-2805-6\">10.1007/s00220-016-2805-6</a>.","ama":"Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal scale. <i>Communications in Mathematical Physics</i>. 2017;349(3):947-990. doi:<a href=\"https://doi.org/10.1007/s00220-016-2805-6\">10.1007/s00220-016-2805-6</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” <i>Communications in Mathematical Physics</i>, vol. 349, no. 3. Springer, pp. 947–990, 2017.","short":"Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990."},"issue":"3","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"02","department":[{"_id":"LaEr"}],"file":[{"file_id":"5102","file_size":1033743,"date_created":"2018-12-12T10:14:47Z","creator":"system","date_updated":"2020-07-14T12:44:39Z","relation":"main_file","checksum":"ddff79154c3daf27237de5383b1264a9","file_name":"IST-2016-722-v1+1_s00220-016-2805-6.pdf","access_level":"open_access","content_type":"application/pdf"}],"page":"947 - 990","ddc":["530"],"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00220-016-2805-6","publisher":"Springer","_id":"1207","date_updated":"2023-09-20T11:16:57Z","type":"journal_article","status":"public","publication":"Communications in Mathematical Physics","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"date_published":"2017-02-01T00:00:00Z","year":"2017","isi":1,"external_id":{"isi":["000393696700005"]},"publist_id":"6141"},{"month":"08","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","issue":"3","citation":{"ista":"Bao Z, Erdös L, Schnelli K. 2016. Local stability of the free additive convolution. Journal of Functional Analysis. 271(3), 672–719.","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>.","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>","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>.","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>","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.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016) 672–719."},"oa_version":"Preprint","title":"Local stability of the free additive convolution","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-0954-3231","first_name":"Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin"}],"scopus_import":1,"day":"01","date_created":"2018-12-11T11:52:00Z","volume":271,"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"}],"intvolume":"       271","publication_status":"published","year":"2016","publist_id":"5764","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"status":"public","publication":"Journal of Functional Analysis","date_published":"2016-08-01T00:00:00Z","ec_funded":1,"publisher":"Academic Press","doi":"10.1016/j.jfa.2016.04.006","type":"journal_article","date_updated":"2021-01-12T06:50:42Z","_id":"1434","page":"672 - 719","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1508.05905","open_access":"1"}]},{"quality_controlled":"1","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1312.5119","open_access":"1"}],"intvolume":"        43","abstract":[{"text":"Let Q = (Q1, . . . , Qn) be a random vector drawn from the uniform distribution on the set of all n! permutations of {1, 2, . . . , n}. Let Z = (Z1, . . . , Zn), where Zj is the mean zero variance one random variable obtained by centralizing and normalizing Qj , j = 1, . . . , n. Assume that Xi , i = 1, . . . ,p are i.i.d. copies of 1/√ p Z and X = Xp,n is the p × n random matrix with Xi as its ith row. Then Sn = XX is called the p × n Spearman's rank correlation matrix which can be regarded as a high dimensional extension of the classical nonparametric statistic Spearman's rank correlation coefficient between two independent random variables. In this paper, we establish a CLT for the linear spectral statistics of this nonparametric random matrix model in the scenario of high dimension, namely, p = p(n) and p/n→c ∈ (0,∞) as n→∞.We propose a novel evaluation scheme to estimate the core quantity in Anderson and Zeitouni's cumulant method in [Ann. Statist. 36 (2008) 2553-2576] to bypass the so-called joint cumulant summability. In addition, we raise a two-step comparison approach to obtain the explicit formulae for the mean and covariance functions in the CLT. Relying on this CLT, we then construct a distribution-free statistic to test complete independence for components of random vectors. Owing to the nonparametric property, we can use this test on generally distributed random variables including the heavy-tailed ones.","lang":"eng"}],"page":"2588 - 2623","date_created":"2018-12-11T11:52:24Z","type":"journal_article","_id":"1504","volume":43,"date_updated":"2021-01-12T06:51:14Z","oa_version":"Published Version","title":"Spectral statistics of large dimensional spearman s rank correlation matrix and its application","publisher":"Institute of Mathematical Statistics","day":"01","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Lin, Liang","last_name":"Lin","first_name":"Liang"},{"first_name":"Guangming","last_name":"Pan","full_name":"Pan, Guangming"},{"last_name":"Zhou","full_name":"Zhou, Wang","first_name":"Wang"}],"doi":"10.1214/15-AOS1353","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2015-12-01T00:00:00Z","citation":{"mla":"Bao, Zhigang, et al. “Spectral Statistics of Large Dimensional Spearman s Rank Correlation Matrix and Its Application.” <i>Annals of Statistics</i>, vol. 43, no. 6, Institute of Mathematical Statistics, 2015, pp. 2588–623, doi:<a href=\"https://doi.org/10.1214/15-AOS1353\">10.1214/15-AOS1353</a>.","apa":"Bao, Z., Lin, L., Pan, G., &#38; Zhou, W. (2015). Spectral statistics of large dimensional spearman s rank correlation matrix and its application. <i>Annals of Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/15-AOS1353\">https://doi.org/10.1214/15-AOS1353</a>","ista":"Bao Z, Lin L, Pan G, Zhou W. 2015. Spectral statistics of large dimensional spearman s rank correlation matrix and its application. Annals of Statistics. 43(6), 2588–2623.","chicago":"Bao, Zhigang, Liang Lin, Guangming Pan, and Wang Zhou. “Spectral Statistics of Large Dimensional Spearman s Rank Correlation Matrix and Its Application.” <i>Annals of Statistics</i>. Institute of Mathematical Statistics, 2015. <a href=\"https://doi.org/10.1214/15-AOS1353\">https://doi.org/10.1214/15-AOS1353</a>.","short":"Z. Bao, L. Lin, G. Pan, W. Zhou, Annals of Statistics 43 (2015) 2588–2623.","ieee":"Z. Bao, L. Lin, G. Pan, and W. Zhou, “Spectral statistics of large dimensional spearman s rank correlation matrix and its application,” <i>Annals of Statistics</i>, vol. 43, no. 6. Institute of Mathematical Statistics, pp. 2588–2623, 2015.","ama":"Bao Z, Lin L, Pan G, Zhou W. Spectral statistics of large dimensional spearman s rank correlation matrix and its application. <i>Annals of Statistics</i>. 2015;43(6):2588-2623. doi:<a href=\"https://doi.org/10.1214/15-AOS1353\">10.1214/15-AOS1353</a>"},"issue":"6","publication":"Annals of Statistics","status":"public","extern":"1","language":[{"iso":"eng"}],"oa":1,"publist_id":"5674","month":"12","year":"2015"},{"type":"journal_article","date_created":"2018-12-11T11:52:25Z","date_updated":"2021-01-12T06:51:14Z","_id":"1505","volume":43,"oa_version":"Preprint","publisher":"Institute of Mathematical Statistics","title":"Universality for the largest eigenvalue of sample covariance matrices with general population","author":[{"first_name":"Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang"},{"last_name":"Pan","full_name":"Pan, Guangming","first_name":"Guangming"},{"first_name":"Wang","full_name":"Zhou, Wang","last_name":"Zhou"}],"doi":"10.1214/14-AOS1281","day":"01","quality_controlled":"1","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1304.5690"}],"intvolume":"        43","abstract":[{"text":"This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form W N =Σ 1/2XX∗Σ 1/2 . Here, X = (xij )M,N is an M× N random matrix with independent entries xij , 1 ≤ i M,≤ 1 ≤ j ≤ N such that Exij = 0, E|xij |2 = 1/N . On dimensionality, we assume that M = M(N) and N/M → d ε (0, ∞) as N ∞→. For a class of general deterministic positive-definite M × M matrices Σ , under some additional assumptions on the distribution of xij 's, we show that the limiting behavior of the largest eigenvalue of W N is universal, via pursuing a Green function comparison strategy raised in [Probab. Theory Related Fields 154 (2012) 341-407, Adv. Math. 229 (2012) 1435-1515] by Erd″os, Yau and Yin for Wigner matrices and extended by Pillai and Yin [Ann. Appl. Probab. 24 (2014) 935-1001] to sample covariance matrices in the null case (&amp;Epsi = I ). Consequently, in the standard complex case (Ex2 ij = 0), combing this universality property and the results known for Gaussian matrices obtained by El Karoui in [Ann. Probab. 35 (2007) 663-714] (nonsingular case) and Onatski in [Ann. Appl. Probab. 18 (2008) 470-490] (singular case), we show that after an appropriate normalization the largest eigenvalue of W N converges weakly to the type 2 Tracy-Widom distribution TW2 . Moreover, in the real case, we show that whenΣ is spiked with a fixed number of subcritical spikes, the type 1 Tracy-Widom limit TW1 holds for the normalized largest eigenvalue of W N , which extends a result of Féral and Péché in [J. Math. Phys. 50 (2009) 073302] to the scenario of nondiagonal Σ and more generally distributed X . In summary, we establish the Tracy-Widom type universality for the largest eigenvalue of generally distributed sample covariance matrices under quite light assumptions on &amp;Sigma . Applications of these limiting results to statistical signal detection and structure recognition of separable covariance matrices are also discussed.","lang":"eng"}],"page":"382 - 421","publist_id":"5672","department":[{"_id":"LaEr"}],"month":"02","year":"2015","acknowledgement":"B.Z. was supported  in  part  by  NSFC  Grant  11071213,  ZJNSF  Grant  R6090034  and  SRFDP  Grant 20100101110001. P.G. was supported in part by the Ministry of Education, Singapore, under Grant ARC 14/11. Z.W. was supported  in  part  by  the  Ministry  of  Education,  Singapore,  under  Grant  ARC  14/11,  and  by a Grant R-155-000-131-112 at the National University of Singapore\r\n","date_published":"2015-02-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","citation":{"ista":"Bao Z, Pan G, Zhou W. 2015. Universality for the largest eigenvalue of sample covariance matrices with general population. Annals of Statistics. 43(1), 382–421.","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “Universality for the Largest Eigenvalue of Sample Covariance Matrices with General Population.” <i>Annals of Statistics</i>. Institute of Mathematical Statistics, 2015. <a href=\"https://doi.org/10.1214/14-AOS1281\">https://doi.org/10.1214/14-AOS1281</a>.","mla":"Bao, Zhigang, et al. “Universality for the Largest Eigenvalue of Sample Covariance Matrices with General Population.” <i>Annals of Statistics</i>, vol. 43, no. 1, Institute of Mathematical Statistics, 2015, pp. 382–421, doi:<a href=\"https://doi.org/10.1214/14-AOS1281\">10.1214/14-AOS1281</a>.","apa":"Bao, Z., Pan, G., &#38; Zhou, W. (2015). Universality for the largest eigenvalue of sample covariance matrices with general population. <i>Annals of Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/14-AOS1281\">https://doi.org/10.1214/14-AOS1281</a>","ama":"Bao Z, Pan G, Zhou W. Universality for the largest eigenvalue of sample covariance matrices with general population. <i>Annals of Statistics</i>. 2015;43(1):382-421. doi:<a href=\"https://doi.org/10.1214/14-AOS1281\">10.1214/14-AOS1281</a>","short":"Z. Bao, G. Pan, W. Zhou, Annals of Statistics 43 (2015) 382–421.","ieee":"Z. Bao, G. Pan, and W. Zhou, “Universality for the largest eigenvalue of sample covariance matrices with general population,” <i>Annals of Statistics</i>, vol. 43, no. 1. Institute of Mathematical Statistics, pp. 382–421, 2015."},"language":[{"iso":"eng"}],"publication":"Annals of Statistics","status":"public","oa":1},{"abstract":[{"lang":"eng","text":"Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i, j = 1, . . . , n} is a collection of independent real random variables with means zero and variances one. Under the additional moment condition supn max1≤i,j ≤n Ea4ij &lt;∞, we prove Girko's logarithmic law of det An in the sense that as n→∞ log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1)."}],"intvolume":"        21","page":"1600 - 1628","quality_controlled":"1","publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/1208.5823","open_access":"1"}],"oa_version":"Preprint","title":"The logarithmic law of random determinant","publisher":"Bernoulli Society for Mathematical Statistics and Probability","doi":"10.3150/14-BEJ615","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475"},{"first_name":"Guangming","last_name":"Pan","full_name":"Pan, Guangming"},{"first_name":"Wang","full_name":"Zhou, Wang","last_name":"Zhou"}],"day":"01","type":"journal_article","date_created":"2018-12-11T11:52:25Z","date_updated":"2021-01-12T06:51:14Z","_id":"1506","volume":21,"language":[{"iso":"eng"}],"status":"public","publication":"Bernoulli","oa":1,"date_published":"2015-08-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","citation":{"ista":"Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli. 21(3), 1600–1628.","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “The Logarithmic Law of Random Determinant.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2015. <a href=\"https://doi.org/10.3150/14-BEJ615\">https://doi.org/10.3150/14-BEJ615</a>.","apa":"Bao, Z., Pan, G., &#38; Zhou, W. (2015). The logarithmic law of random determinant. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/14-BEJ615\">https://doi.org/10.3150/14-BEJ615</a>","mla":"Bao, Zhigang, et al. “The Logarithmic Law of Random Determinant.” <i>Bernoulli</i>, vol. 21, no. 3, Bernoulli Society for Mathematical Statistics and Probability, 2015, pp. 1600–28, doi:<a href=\"https://doi.org/10.3150/14-BEJ615\">10.3150/14-BEJ615</a>.","ama":"Bao Z, Pan G, Zhou W. The logarithmic law of random determinant. <i>Bernoulli</i>. 2015;21(3):1600-1628. doi:<a href=\"https://doi.org/10.3150/14-BEJ615\">10.3150/14-BEJ615</a>","ieee":"Z. Bao, G. Pan, and W. Zhou, “The logarithmic law of random determinant,” <i>Bernoulli</i>, vol. 21, no. 3. Bernoulli Society for Mathematical Statistics and Probability, pp. 1600–1628, 2015.","short":"Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628."},"month":"08","year":"2015","publist_id":"5671","department":[{"_id":"LaEr"}]},{"year":"2015","month":"06","department":[{"_id":"LaEr"}],"publist_id":"5586","language":[{"iso":"eng"}],"status":"public","publication":"IEEE Transactions on Information Theory","citation":{"ama":"Bao Z, Pan G, Zhou W. Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. <i>IEEE Transactions on Information Theory</i>. 2015;61(6):3413-3426. doi:<a href=\"https://doi.org/10.1109/TIT.2015.2421894\">10.1109/TIT.2015.2421894</a>","short":"Z. Bao, G. Pan, W. Zhou, IEEE Transactions on Information Theory 61 (2015) 3413–3426.","ieee":"Z. Bao, G. Pan, and W. Zhou, “Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices,” <i>IEEE Transactions on Information Theory</i>, vol. 61, no. 6. IEEE, pp. 3413–3426, 2015.","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “Asymptotic Mutual Information Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2015. <a href=\"https://doi.org/10.1109/TIT.2015.2421894\">https://doi.org/10.1109/TIT.2015.2421894</a>.","ista":"Bao Z, Pan G, Zhou W. 2015. Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on Information Theory. 61(6), 3413–3426.","mla":"Bao, Zhigang, et al. “Asymptotic Mutual Information Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” <i>IEEE Transactions on Information Theory</i>, vol. 61, no. 6, IEEE, 2015, pp. 3413–26, doi:<a href=\"https://doi.org/10.1109/TIT.2015.2421894\">10.1109/TIT.2015.2421894</a>.","apa":"Bao, Z., Pan, G., &#38; Zhou, W. (2015). Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2015.2421894\">https://doi.org/10.1109/TIT.2015.2421894</a>"},"issue":"6","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"G. Pan was supported by MOE Tier 2 under Grant 2014-T2-2-060 and in part by Tier 1 under Grant RG25/14 through the Nanyang Technological University, Singapore. W. Zhou was supported by the National University of Singapore, Singapore, under Grant R-155-000-131-112.\r\n","date_published":"2015-06-01T00:00:00Z","scopus_import":1,"day":"01","author":[{"orcid":"0000-0003-3036-1475","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","last_name":"Bao"},{"full_name":"Pan, Guangming","last_name":"Pan","first_name":"Guangming"},{"first_name":"Wang","full_name":"Zhou, Wang","last_name":"Zhou"}],"doi":"10.1109/TIT.2015.2421894","publisher":"IEEE","title":"Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices","oa_version":"None","volume":61,"_id":"1585","date_updated":"2021-01-12T06:51:46Z","date_created":"2018-12-11T11:52:52Z","type":"journal_article","page":"3413 - 3426","intvolume":"        61","abstract":[{"text":"In this paper, we consider the fluctuation of mutual information statistics of a multiple input multiple output channel communication systems without assuming that the entries of the channel matrix have zero pseudovariance. To this end, we also establish a central limit theorem of the linear spectral statistics for sample covariance matrices under general moment conditions by removing the restrictions imposed on the second moment and fourth moment on the matrix entries in Bai and Silverstein (2004).","lang":"eng"}],"quality_controlled":"1","publication_status":"published"}]