[{"dc":{"rights":["info:eu-repo/semantics/openAccess"],"source":["Erdös L, Knowles A, Yau H, Yin J. Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics. 2013;323(1):367-416. doi:10.1007/s00220-013-1773-3"],"title":["Delocalization and diffusion profile for random band matrices"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/s00220-013-1773-3"],"publisher":["Springer"],"date":["2013"],"identifier":["https://research-explorer.ista.ac.at/record/2697"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"description":["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."],"creator":["László Erdös","Knowles, Antti","Yau, Horng-Tzer","Yin, Jun"]},"uri_base":"https://research-explorer.ista.ac.at","day":"01","month":"10","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1205.5669"}],"citation":{"mla":"Erdös, László, et al. “Delocalization and Diffusion Profile for Random Band Matrices.” Communications in Mathematical Physics, vol. 323, no. 1, Springer, 2013, pp. 367–416, doi:10.1007/s00220-013-1773-3.","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.” Communications in Mathematical Physics. Springer, 2013. https://doi.org/10.1007/s00220-013-1773-3.","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.","apa":"Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-013-1773-3","ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “Delocalization and diffusion profile for random band matrices,” Communications in Mathematical Physics, vol. 323, no. 1. Springer, pp. 367–416, 2013."},"publication":"Communications in Mathematical Physics","page":"367 - 416","quality_controlled":0,"date_published":"2013-10-01T00:00:00Z","type":"journal_article","issue":"1","publist_id":"4199","abstract":[{"lang":"eng"}],"extern":1,"_id":"2697","intvolume":" 323","status":"public","publication_status":"published","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Knowles","first_name":"Antti"},{"first_name":"Horng","last_name":"Yau"},{"last_name":"Yin","first_name":"Jun"}],"volume":323,"dini_type":"doc-type:article","date_updated":"2021-01-12T06:59:07Z","date_created":"2018-12-11T11:59:07Z"}]