{"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"first_name":"Antti","last_name":"Knowles","full_name":"Knowles, Antti"}],"issue":"3","department":[{"_id":"LaEr"}],"main_file_link":[{"url":"http://arxiv.org/abs/1309.5106","open_access":"1"}],"oa":1,"publication_status":"published","scopus_import":1,"_id":"2166","abstract":[{"lang":"eng","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). "}],"date_created":"2018-12-11T11:56:05Z","language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:55:43Z","date_published":"2015-02-01T00:00:00Z","citation":{"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.","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","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.","short":"L. Erdös, A. Knowles, Communications in Mathematical Physics 333 (2015) 1365–1416.","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.","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"},"title":"The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case","year":"2015","type":"journal_article","intvolume":" 333","publisher":"Springer","publication":"Communications in Mathematical Physics","oa_version":"Preprint","month":"02","status":"public","page":"1365 - 1416","doi":"10.1007/s00220-014-2119-5","quality_controlled":"1","publist_id":"4818","day":"01","volume":333,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}