{"year":"1998","type":"journal_article","author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"title":"Lifschitz tail in a magnetic field: The nonclassical regime","_id":"2728","date_updated":"2022-08-30T08:17:54Z","page":"321 - 371","month":"11","volume":112,"date_created":"2018-12-11T11:59:17Z","extern":"1","intvolume":"       112","article_type":"original","acknowledgement":"The author is grateful to Professor A.-S. Sznitman for explaining him his work and for fruitful discussions, and to the referee for pointing out errors and for many helpful comments.This work has been initiated and later on completed at the Forschungsinstitut für Mathematik, ETH Zürich.","publication_status":"published","oa_version":"None","day":"01","status":"public","date_published":"1998-11-01T00:00:00Z","publication_identifier":{"issn":["0044-3719"]},"quality_controlled":"1","publication":"Probability Theory and Related Fields","article_processing_charge":"No","language":[{"iso":"eng"}],"issue":"3","publisher":"Springer","publist_id":"4163","abstract":[{"text":"We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional magnetic Schrödinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom of the spectrum. This result complements the earlier (nonrigorous) calculations by Brézin, Gross and Itzykson which predict that the IDS is discontinuous at the bottom of the spectrum for zero range (Dirac delta) impurities at low density. We also elucidate the reason behind this apparent controversy. Our methods involve magnetic localization techniques (both in space and energy) in addition to a modified version of the &quot;enlargement of obstacles&quot; method developed by A.-S. Sznitman.","lang":"eng"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","doi":"10.1007/s004400050193","scopus_import":"1","citation":{"short":"L. Erdös, Probability Theory and Related Fields 112 (1998) 321–371.","apa":"Erdös, L. (1998). Lifschitz tail in a magnetic field: The nonclassical regime. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s004400050193\">https://doi.org/10.1007/s004400050193</a>","mla":"Erdös, László. “Lifschitz Tail in a Magnetic Field: The Nonclassical Regime.” <i>Probability Theory and Related Fields</i>, vol. 112, no. 3, Springer, 1998, pp. 321–71, doi:<a href=\"https://doi.org/10.1007/s004400050193\">10.1007/s004400050193</a>.","ista":"Erdös L. 1998. Lifschitz tail in a magnetic field: The nonclassical regime. Probability Theory and Related Fields. 112(3), 321–371.","ieee":"L. Erdös, “Lifschitz tail in a magnetic field: The nonclassical regime,” <i>Probability Theory and Related Fields</i>, vol. 112, no. 3. Springer, pp. 321–371, 1998.","ama":"Erdös L. Lifschitz tail in a magnetic field: The nonclassical regime. <i>Probability Theory and Related Fields</i>. 1998;112(3):321-371. doi:<a href=\"https://doi.org/10.1007/s004400050193\">10.1007/s004400050193</a>","chicago":"Erdös, László. “Lifschitz Tail in a Magnetic Field: The Nonclassical Regime.” <i>Probability Theory and Related Fields</i>. Springer, 1998. <a href=\"https://doi.org/10.1007/s004400050193\">https://doi.org/10.1007/s004400050193</a>."}}