{"date_updated":"2021-01-12T06:59:40Z","quality_controlled":0,"main_file_link":[{"url":"http://arxiv.org/abs/1205.5664","open_access":"1"}],"_id":"2780","publication":"Annales Henri Poincare","abstract":[{"lang":"eng","text":"We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix entries. Our results generalize the previous results of Erdős et al. (Ann Probab, arXiv:1103.1919, 2013; Commun Math Phys, arXiv:1103.3869, 2013; J Combin 1(2):15-85, 2011) which constituted a key step in the proof of the local semicircle law with optimal error bound in mean-field random matrix models. Our bounds apply to random band matrices and improve previous estimates from order 2 to order 4 in the cases relevant to applications. In particular, they lead to a proof of the diffusion approximation for the magnitude of the resolvent of random band matrices. This, in turn, implies new delocalization bounds on the eigenvectors. The applications are presented in a separate paper (Erdős et al., arXiv:1205.5669, 2013)."}],"issue":"8","doi":"10.1007/s00023-013-0235-y","publist_id":"4110","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"László Erdös"},{"first_name":"Antti","last_name":"Knowles","full_name":"Knowles, Antti"},{"first_name":"Horng","full_name":"Yau, Horng-Tzer","last_name":"Yau"}],"citation":{"ieee":"L. Erdös, A. Knowles, and H. Yau, “Averaging fluctuations in resolvents of random band matrices,” <i>Annales Henri Poincare</i>, vol. 14, no. 8. Birkhäuser, pp. 1837–1926, 2013.","mla":"Erdös, László, et al. “Averaging Fluctuations in Resolvents of Random Band Matrices.” <i>Annales Henri Poincare</i>, vol. 14, no. 8, Birkhäuser, 2013, pp. 1837–926, doi:<a href=\"https://doi.org/10.1007/s00023-013-0235-y\">10.1007/s00023-013-0235-y</a>.","apa":"Erdös, L., Knowles, A., &#38; Yau, H. (2013). Averaging fluctuations in resolvents of random band matrices. <i>Annales Henri Poincare</i>. Birkhäuser. <a href=\"https://doi.org/10.1007/s00023-013-0235-y\">https://doi.org/10.1007/s00023-013-0235-y</a>","chicago":"Erdös, László, Antti Knowles, and Horng Yau. “Averaging Fluctuations in Resolvents of Random Band Matrices.” <i>Annales Henri Poincare</i>. Birkhäuser, 2013. <a href=\"https://doi.org/10.1007/s00023-013-0235-y\">https://doi.org/10.1007/s00023-013-0235-y</a>.","short":"L. Erdös, A. Knowles, H. Yau, Annales Henri Poincare 14 (2013) 1837–1926.","ama":"Erdös L, Knowles A, Yau H. Averaging fluctuations in resolvents of random band matrices. <i>Annales Henri Poincare</i>. 2013;14(8):1837-1926. doi:<a href=\"https://doi.org/10.1007/s00023-013-0235-y\">10.1007/s00023-013-0235-y</a>","ista":"Erdös L, Knowles A, Yau H. 2013. Averaging fluctuations in resolvents of random band matrices. Annales Henri Poincare. 14(8), 1837–1926."},"intvolume":"        14","page":"1837 - 1926","status":"public","title":"Averaging fluctuations in resolvents of random band matrices","extern":1,"publication_status":"published","year":"2013","publisher":"Birkhäuser","volume":14,"type":"journal_article","day":"01","month":"12","date_created":"2018-12-11T11:59:33Z","date_published":"2013-12-01T00:00:00Z","oa":1}