{"abstract":[{"text":"We consider Hermitian and symmetric random band matrices H = (h xy ) in d⩾1 d ⩾ 1 dimensions. The matrix entries h xy , indexed by x,y∈(Z/LZ)d x , y ∈ ( Z / L Z ) d , are independent, centred random variables with variances sxy=E|hxy|2 s x y = E | h x y | 2 . We assume that s xy is negligible if |x − y| exceeds the band width W. In one dimension we prove that the eigenvectors of H are delocalized if W≫L4/5 W ≫ L 4 / 5 . We also show that the magnitude of the matrix entries |Gxy|2 | G x y | 2 of the resolvent G=G(z)=(H−z)−1 G = G ( z ) = ( H - z ) - 1 is self-averaging and we compute E|Gxy|2 E | G x y | 2 . We show that, as L→∞ L → ∞ and W≫L4/5 W ≫ L 4 / 5 , the behaviour of E|Gxy|2 E | G x y | 2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions.","lang":"eng"}],"publisher":"Springer","date_published":"2013-10-01T00:00:00Z","month":"10","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"László Erdös"},{"full_name":"Knowles, Antti","last_name":"Knowles","first_name":"Antti"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng-Tzer"},{"full_name":"Yin, Jun","first_name":"Jun","last_name":"Yin"}],"day":"01","date_updated":"2021-01-12T06:59:07Z","extern":1,"issue":"1","_id":"2697","main_file_link":[{"url":"http://arxiv.org/abs/1205.5669","open_access":"1"}],"publication_status":"published","publist_id":"4199","volume":323,"quality_controlled":0,"citation":{"ama":"Erdös L, Knowles A, Yau H, Yin J. Delocalization and diffusion profile for random band matrices. <i>Communications in Mathematical Physics</i>. 2013;323(1):367-416. doi:<a href=\"https://doi.org/10.1007/s00220-013-1773-3\">10.1007/s00220-013-1773-3</a>","ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “Delocalization and diffusion profile for random band matrices,” <i>Communications in Mathematical Physics</i>, vol. 323, no. 1. Springer, pp. 367–416, 2013.","apa":"Erdös, L., Knowles, A., Yau, H., &#38; Yin, J. (2013). Delocalization and diffusion profile for random band matrices. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-013-1773-3\">https://doi.org/10.1007/s00220-013-1773-3</a>","short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics 323 (2013) 367–416.","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Delocalization and Diffusion Profile for Random Band Matrices.” <i>Communications in Mathematical Physics</i>. Springer, 2013. <a href=\"https://doi.org/10.1007/s00220-013-1773-3\">https://doi.org/10.1007/s00220-013-1773-3</a>.","mla":"Erdös, László, et al. “Delocalization and Diffusion Profile for Random Band Matrices.” <i>Communications in Mathematical Physics</i>, vol. 323, no. 1, Springer, 2013, pp. 367–416, doi:<a href=\"https://doi.org/10.1007/s00220-013-1773-3\">10.1007/s00220-013-1773-3</a>.","ista":"Erdös L, Knowles A, Yau H, Yin J. 2013. Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics. 323(1), 367–416."},"intvolume":"       323","date_created":"2018-12-11T11:59:07Z","year":"2013","oa":1,"status":"public","doi":"10.1007/s00220-013-1773-3","type":"journal_article","page":"367 - 416","publication":"Communications in Mathematical Physics","title":"Delocalization and diffusion profile for random band matrices"}