{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"oa_version":"Preprint","abstract":[{"text":"We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014). ","lang":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1309.5106","open_access":"1"}],"publication_status":"published","_id":"2166","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"full_name":"Knowles, Antti","first_name":"Antti","last_name":"Knowles"}],"scopus_import":1,"publisher":"Springer","date_created":"2018-12-11T11:56:05Z","title":"The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case","month":"02","year":"2015","issue":"3","language":[{"iso":"eng"}],"citation":{"ama":"Erdös L, Knowles A. The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. *Communications in Mathematical Physics*. 2015;333(3):1365-1416. doi:10.1007/s00220-014-2119-5","mla":"Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices I: The Unimodular Case.” *Communications in Mathematical Physics*, vol. 333, no. 3, Springer, 2015, pp. 1365–416, doi:10.1007/s00220-014-2119-5.","ieee":"L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case,” *Communications in Mathematical Physics*, vol. 333, no. 3. Springer, pp. 1365–1416, 2015.","apa":"Erdös, L., & Knowles, A. (2015). The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-014-2119-5","short":"L. Erdös, A. Knowles, Communications in Mathematical Physics 333 (2015) 1365–1416.","chicago":"Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices I: The Unimodular Case.” *Communications in Mathematical Physics*. Springer, 2015. https://doi.org/10.1007/s00220-014-2119-5.","ista":"Erdös L, Knowles A. 2015. The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics. 333(3), 1365–1416."},"quality_controlled":"1","day":"01","date_updated":"2021-01-12T06:55:43Z","intvolume":" 333","page":"1365 - 1416","doi":"10.1007/s00220-014-2119-5","volume":333,"oa":1,"type":"journal_article","status":"public","date_published":"2015-02-01T00:00:00Z","publist_id":"4818","publication":"Communications in Mathematical Physics"}