[{"author":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László"}],"publication":"Proceedings of the International Congress of Mathematicians","scopus_import":"1","conference":{"start_date":"2014-08-13","name":"ICM: International Congress of Mathematicians","end_date":"2014-08-21","location":"Seoul, Korea"},"type":"conference","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1407.5752"}],"title":"Random matrices, log-gases and Hölder regularity","oa":1,"month":"08","publication_status":"published","volume":3,"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"page":"214 - 236","quality_controlled":"1","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"No","date_created":"2018-12-11T11:52:25Z","ec_funded":1,"abstract":[{"text":"The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large real and complex Hermitian matrices with independent, identically distributed entries are universal in a sense that they depend only on the symmetry class of the matrix and otherwise are independent of the details of the distribution. We present the recent solution to this half-century old conjecture. We explain how stochastic tools, such as the Dyson Brownian motion, and PDE ideas, such as De Giorgi-Nash-Moser regularity theory, were combined in the solution. We also show related results for log-gases that represent a universal model for strongly correlated systems. Finally, in the spirit of Wigner’s original vision, we discuss the extensions of these universality results to more realistic physical systems such as random band matrices.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"5670","date_updated":"2025-06-11T07:52:59Z","date_published":"2014-08-01T00:00:00Z","publisher":"International Congress of Mathematicians","acknowledgement":"The author is partially supported by SFB-TR 12 Grant of the German Research Council.","year":"2014","citation":{"ista":"Erdös L. 2014. Random matrices, log-gases and Hölder regularity. Proceedings of the International Congress of Mathematicians. ICM: International Congress of Mathematicians vol. 3, 214–236.","ama":"Erdös L. Random matrices, log-gases and Hölder regularity. In: Proceedings of the International Congress of Mathematicians. Vol 3. International Congress of Mathematicians; 2014:214-236.","apa":"Erdös, L. (2014). Random matrices, log-gases and Hölder regularity. In Proceedings of the International Congress of Mathematicians (Vol. 3, pp. 214–236). Seoul, Korea: International Congress of Mathematicians.","ieee":"L. Erdös, “Random matrices, log-gases and Hölder regularity,” in Proceedings of the International Congress of Mathematicians, Seoul, Korea, 2014, vol. 3, pp. 214–236.","chicago":"Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” In Proceedings of the International Congress of Mathematicians, 3:214–36. International Congress of Mathematicians, 2014.","short":"L. Erdös, in:, Proceedings of the International Congress of Mathematicians, International Congress of Mathematicians, 2014, pp. 214–236.","mla":"Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” Proceedings of the International Congress of Mathematicians, vol. 3, International Congress of Mathematicians, 2014, pp. 214–36."},"arxiv":1,"day":"01","oa_version":"Submitted Version","status":"public","_id":"1507","intvolume":" 3","external_id":{"arxiv":["1407.5752"]}},{"type":"journal_article","doi":"10.1007/s11040-014-9163-4","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1304.3862"}],"title":"Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips","oa":1,"scopus_import":"1","corr_author":"1","author":[{"full_name":"Sadel, Christian","last_name":"Sadel","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8255-3968","first_name":"Christian"}],"publication":"Mathematical Physics, Analysis and Geometry","article_processing_charge":"No","date_created":"2018-12-11T11:54:45Z","quality_controlled":"1","project":[{"name":"NSERC Postdoctoral fellowship","_id":"26450934-B435-11E9-9278-68D0E5697425"},{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"volume":17,"page":"409 - 440","month":"12","fulldoi":"https://doi.org/10.1007/s11040-014-9163-4","article_type":"original","date_published":"2014-12-17T00:00:00Z","date_updated":"2025-09-29T12:14:12Z","publist_id":"5168","abstract":[{"text":"We consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random Schrödinger operators on such tree-strips have purely absolutely continuous spectrum in a certain set.","lang":"eng"}],"ec_funded":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":" 17","issue":"3-4","external_id":{"arxiv":["1304.3862"],"isi":["000348286700010"]},"oa_version":"Preprint","status":"public","_id":"1926","publisher":"Springer","citation":{"ista":"Sadel C. 2014. Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. 17(3–4), 409–440.","ama":"Sadel C. Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. 2014;17(3-4):409-440. doi:10.1007/s11040-014-9163-4","apa":"Sadel, C. (2014). Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-014-9163-4","ieee":"C. Sadel, “Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 409–440, 2014.","chicago":"Sadel, Christian. “Absolutely Continuous Spectrum for Random Schrödinger Operators on the Fibonacci and Similar Tree-Strips.” Mathematical Physics, Analysis and Geometry. Springer, 2014. https://doi.org/10.1007/s11040-014-9163-4.","short":"C. Sadel, Mathematical Physics, Analysis and Geometry 17 (2014) 409–440.","mla":"Sadel, Christian. “Absolutely Continuous Spectrum for Random Schrödinger Operators on the Fibonacci and Similar Tree-Strips.” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4, Springer, 2014, pp. 409–40, doi:10.1007/s11040-014-9163-4."},"year":"2014","isi":1,"arxiv":1,"day":"17"},{"external_id":{"isi":["000341491700007"],"arxiv":["1306.5728"]},"issue":"1","intvolume":" 332","status":"public","_id":"1937","oa_version":"Submitted Version","day":"01","arxiv":1,"isi":1,"citation":{"mla":"Bourgade, Paul, et al. “Edge Universality of Beta Ensembles.” Communications in Mathematical Physics, vol. 332, no. 1, Springer, 2014, pp. 261–353, doi:10.1007/s00220-014-2120-z.","short":"P. Bourgade, L. Erdös, H. Yau, Communications in Mathematical Physics 332 (2014) 261–353.","chicago":"Bourgade, Paul, László Erdös, and Horngtzer Yau. “Edge Universality of Beta Ensembles.” Communications in Mathematical Physics. Springer, 2014. https://doi.org/10.1007/s00220-014-2120-z.","apa":"Bourgade, P., Erdös, L., & Yau, H. (2014). Edge universality of beta ensembles. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-014-2120-z","ieee":"P. Bourgade, L. Erdös, and H. Yau, “Edge universality of beta ensembles,” Communications in Mathematical Physics, vol. 332, no. 1. Springer, pp. 261–353, 2014.","ama":"Bourgade P, Erdös L, Yau H. Edge universality of beta ensembles. Communications in Mathematical Physics. 2014;332(1):261-353. doi:10.1007/s00220-014-2120-z","ista":"Bourgade P, Erdös L, Yau H. 2014. Edge universality of beta ensembles. Communications in Mathematical Physics. 332(1), 261–353."},"year":"2014","publisher":"Springer","date_published":"2014-11-01T00:00:00Z","fulldoi":"https://doi.org/10.1007/s00220-014-2120-z","date_updated":"2025-09-29T12:08:21Z","publist_id":"5158","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","abstract":[{"text":"We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4.","lang":"eng"}],"date_created":"2018-12-11T11:54:48Z","article_processing_charge":"No","project":[{"name":"Glutamaterge synaptische Ãbertragung und Plastizität in hippocampalen Mikroschaltkreisen","_id":"25BDE9A4-B435-11E9-9278-68D0E5697425","grant_number":"SFB-TR3-TP10B"}],"quality_controlled":"1","page":"261 - 353","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"volume":332,"publication_status":"published","month":"11","title":"Edge universality of beta ensembles","oa":1,"doi":"10.1007/s00220-014-2120-z","main_file_link":[{"url":"http://arxiv.org/abs/1306.5728","open_access":"1"}],"type":"journal_article","scopus_import":"1","publication":"Communications in Mathematical Physics","author":[{"last_name":"Bourgade","full_name":"Bourgade, Paul","first_name":"Paul"},{"full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Horngtzer","last_name":"Yau","full_name":"Yau, Horngtzer"}]},{"quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"}],"date_created":"2018-12-11T11:55:15Z","article_processing_charge":"No","month":"12","volume":17,"language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"publication_status":"published","page":"441 - 464","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1407.1552"}],"doi":"10.1007/s11040-014-9164-3","type":"journal_article","title":"Phase transition in the density of states of quantum spin glasses","oa":1,"author":[{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J"}],"publication":"Mathematical Physics, Analysis and Geometry","scopus_import":"1","intvolume":" 17","external_id":{"arxiv":["1407.1552"],"isi":["000348286700011"]},"issue":"3-4","citation":{"chicago":"Erdös, László, and Dominik J Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.” Mathematical Physics, Analysis and Geometry. Springer, 2014. https://doi.org/10.1007/s11040-014-9164-3.","mla":"Erdös, László, and Dominik J. Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4, Springer, 2014, pp. 441–64, doi:10.1007/s11040-014-9164-3.","short":"L. Erdös, D.J. Schröder, Mathematical Physics, Analysis and Geometry 17 (2014) 441–464.","ista":"Erdös L, Schröder DJ. 2014. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 17(3–4), 441–464.","ama":"Erdös L, Schröder DJ. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 2014;17(3-4):441-464. doi:10.1007/s11040-014-9164-3","ieee":"L. Erdös and D. J. Schröder, “Phase transition in the density of states of quantum spin glasses,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 441–464, 2014.","apa":"Erdös, L., & Schröder, D. J. (2014). Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-014-9164-3"},"year":"2014","publisher":"Springer","day":"17","arxiv":1,"isi":1,"oa_version":"Submitted Version","status":"public","_id":"2019","fulldoi":"https://doi.org/10.1007/s11040-014-9164-3","date_published":"2014-12-17T00:00:00Z","abstract":[{"text":"We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of Keating et al. (2014) that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitrary hypergraphs. We test the optimality of our condition on the maximal degree for p-uniform hypergraphs that correspond to p-spin glass Hamiltonians acting on n distinguishable spin- 1/2 particles. At the critical threshold p = n1/2 we find a sharp classical-quantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory.","lang":"eng"}],"ec_funded":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2025-09-29T12:00:05Z","publist_id":"5053"},{"type":"journal_article","doi":"10.1007/s10955-013-0807-8","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1207.0031"}],"title":"Local eigenvalue density for general MANOVA matrices","oa":1,"scopus_import":"1","corr_author":"1","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Brendan","full_name":"Farrell, Brendan","last_name":"Farrell"}],"publication":"Journal of Statistical Physics","article_processing_charge":"No","date_created":"2018-12-11T11:59:34Z","quality_controlled":"1","publication_status":"published","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"volume":152,"page":"1003 - 1032","month":"07","fulldoi":"https://doi.org/10.1007/s10955-013-0807-8","date_published":"2013-07-18T00:00:00Z","publist_id":"4107","date_updated":"2025-09-29T14:07:43Z","abstract":[{"lang":"eng","text":"We consider random n×n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}, where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spectral edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble even on the shortest possible scales of order 1/n (up to log n factors). This result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur law for general MANOVA matrices."}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":" 152","issue":"6","external_id":{"arxiv":["1207.0031"],"isi":["000323203800001"]},"oa_version":"Preprint","_id":"2782","status":"public","publisher":"Springer","citation":{"ama":"Erdös L, Farrell B. Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. 2013;152(6):1003-1032. doi:10.1007/s10955-013-0807-8","ista":"Erdös L, Farrell B. 2013. Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. 152(6), 1003–1032.","apa":"Erdös, L., & Farrell, B. (2013). Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-013-0807-8","ieee":"L. Erdös and B. Farrell, “Local eigenvalue density for general MANOVA matrices,” Journal of Statistical Physics, vol. 152, no. 6. Springer, pp. 1003–1032, 2013.","chicago":"Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General MANOVA Matrices.” Journal of Statistical Physics. Springer, 2013. https://doi.org/10.1007/s10955-013-0807-8.","mla":"Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General MANOVA Matrices.” Journal of Statistical Physics, vol. 152, no. 6, Springer, 2013, pp. 1003–32, doi:10.1007/s10955-013-0807-8.","short":"L. Erdös, B. Farrell, Journal of Statistical Physics 152 (2013) 1003–1032."},"year":"2013","isi":1,"arxiv":1,"day":"18"},{"page":"1-58","pubrep_id":"406","publication_status":"published","department":[{"_id":"LaEr"}],"volume":18,"language":[{"iso":"eng"}],"month":"05","article_processing_charge":"No","date_created":"2018-12-11T11:59:51Z","quality_controlled":"1","scopus_import":"1","publication":"Electronic Journal of Probability","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"last_name":"Knowles","full_name":"Knowles, Antti","first_name":"Antti"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng"},{"full_name":"Yin, Jun","last_name":"Yin","first_name":"Jun"}],"title":"The local semicircle law for a general class of random matrices","oa":1,"type":"journal_article","doi":"10.1214/EJP.v18-2473","status":"public","_id":"2837","oa_version":"Published Version","isi":1,"day":"29","publisher":"Institute of Mathematical Statistics","citation":{"mla":"Erdös, László, et al. “The Local Semicircle Law for a General Class of Random Matrices.” Electronic Journal of Probability, vol. 18, no. 59, Institute of Mathematical Statistics, 2013, pp. 1–58, doi:10.1214/EJP.v18-2473.","short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 18 (2013) 1–58.","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “The Local Semicircle Law for a General Class of Random Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2013. https://doi.org/10.1214/EJP.v18-2473.","apa":"Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). The local semicircle law for a general class of random matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v18-2473","ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a general class of random matrices,” Electronic Journal of Probability, vol. 18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.","ama":"Erdös L, Knowles A, Yau H, Yin J. The local semicircle law for a general class of random matrices. Electronic Journal of Probability. 2013;18(59):1-58. doi:10.1214/EJP.v18-2473","ista":"Erdös L, Knowles A, Yau H, Yin J. 2013. The local semicircle law for a general class of random matrices. Electronic Journal of Probability. 18(59), 1–58."},"year":"2013","issue":"59","external_id":{"isi":["000319561600001"]},"intvolume":" 18","file":[{"file_id":"5169","file_size":651497,"date_created":"2018-12-12T10:15:46Z","file_name":"IST-2016-406-v1+1_2473-13759-1-PB.pdf","checksum":"aac9e52a00cb2f5149dc9e362b5ccf44","access_level":"open_access","relation":"main_file","creator":"system","date_updated":"2020-07-14T12:45:50Z","content_type":"application/pdf"}],"publist_id":"3962","date_updated":"2025-09-29T13:46:52Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","abstract":[{"lang":"eng","text":"We consider a general class of N × N random matrices whose entries hij are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results [17] both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, maxi,j E|hij|2. As a consequence, we prove the universality of the local n-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width W ≫N1-εn with some εn > 0 and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments from [17, 19, 6]."}],"file_date_updated":"2020-07-14T12:45:50Z","has_accepted_license":"1","date_published":"2013-05-29T00:00:00Z","ddc":["530"],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"fulldoi":"https://doi.org/10.1214/EJP.v18-2473"},{"intvolume":" 15","external_id":{"isi":["000326323400006"],"arxiv":["1105.0506"]},"issue":"6","oa_version":"Preprint","status":"public","_id":"2698","citation":{"chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society. EMS Press, 2013. https://doi.org/10.4171/JEMS/416.","mla":"Erdös, László, et al. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society, vol. 15, no. 6, EMS Press, 2013, pp. 2093–113, doi:10.4171/JEMS/416.","short":"L. Erdös, S. Fournais, J. Solovej, Journal of the European Mathematical Society 15 (2013) 2093–2113.","ama":"Erdös L, Fournais S, Solovej J. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 2013;15(6):2093-2113. doi:10.4171/JEMS/416","ista":"Erdös L, Fournais S, Solovej J. 2013. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 15(6), 2093–2113.","apa":"Erdös, L., Fournais, S., & Solovej, J. (2013). Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. EMS Press. https://doi.org/10.4171/JEMS/416","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” Journal of the European Mathematical Society, vol. 15, no. 6. EMS Press, pp. 2093–2113, 2013."},"year":"2013","publisher":"EMS Press","day":"16","arxiv":1,"isi":1,"fulldoi":"https://doi.org/10.4171/JEMS/416","date_published":"2013-10-16T00:00:00Z","publist_id":"4198","date_updated":"2026-07-06T11:56:35Z","abstract":[{"lang":"eng","text":"We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B. The total energy includes the field energy β∫B2 and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter β tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical asymptotics, h→0, of the total ground state energy E(β,h,V). The relevant parameter measuring the field strength in the semiclassical limit is κ=βh. We are not able to give the exact leading order semiclassical asymptotics uniformly in κ or even for fixed κ. We do however give upper and lower bounds on E with almost matching dependence on κ. In the simultaneous limit h→0 and κ→∞ we show that the standard non-magnetic Weyl asymptotics holds. The same result also holds for the spinless case, i.e. where the Pauli operator is replaced by the Schrödinger operator."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:59:07Z","article_processing_charge":"No","quality_controlled":"1","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"volume":15,"publication_status":"published","page":"2093 - 2113","month":"10","doi":"10.4171/JEMS/416","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1105.0506"}],"type":"journal_article","title":"Stability and semiclassics in self-generated fields","oa":1,"author":[{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Søren","last_name":"Fournais","full_name":"Fournais, Søren"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"publication":"Journal of the European Mathematical Society"}]