--- _id: '2773' abstract: - lang: eng text: Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our work [2]. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau citation: ama: Erdös L, Yau H. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 2012;17. doi:10.1214/EJP.v17-1779 apa: Erdös, L., & Yau, H. (2012). A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v17-1779 chicago: Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2012. https://doi.org/10.1214/EJP.v17-1779. ieee: L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices,” Electronic Journal of Probability, vol. 17. Institute of Mathematical Statistics, 2012. ista: Erdös L, Yau H. 2012. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 17. mla: Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability, vol. 17, Institute of Mathematical Statistics, 2012, doi:10.1214/EJP.v17-1779. short: L. Erdös, H. Yau, Electronic Journal of Probability 17 (2012). date_created: 2018-12-11T11:59:31Z date_published: 2012-04-10T00:00:00Z date_updated: 2021-01-12T06:59:36Z day: '10' doi: 10.1214/EJP.v17-1779 extern: 1 intvolume: ' 17' month: '04' publication: Electronic Journal of Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '4117' quality_controlled: 0 status: public title: A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices type: journal_article volume: 17 year: '2012' ... --- _id: '2771' abstract: - lang: eng text: We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdos and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: David full_name: Hasler, David G last_name: Hasler citation: ama: Erdös L, Hasler D. Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. 2012;146(5):900-923. doi:10.1007/s10955-012-0445-6 apa: Erdös, L., & Hasler, D. (2012). Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-012-0445-6 chicago: Erdös, László, and David Hasler. “Anderson Localization at Band Edges for Random Magnetic Fields.” Journal of Statistical Physics. Springer, 2012. https://doi.org/10.1007/s10955-012-0445-6. ieee: L. Erdös and D. Hasler, “Anderson localization at band edges for random magnetic fields,” Journal of Statistical Physics, vol. 146, no. 5. Springer, pp. 900–923, 2012. ista: Erdös L, Hasler D. 2012. Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. 146(5), 900–923. mla: Erdös, László, and David Hasler. “Anderson Localization at Band Edges for Random Magnetic Fields.” Journal of Statistical Physics, vol. 146, no. 5, Springer, 2012, pp. 900–23, doi:10.1007/s10955-012-0445-6. short: L. Erdös, D. Hasler, Journal of Statistical Physics 146 (2012) 900–923. date_created: 2018-12-11T11:59:31Z date_published: 2012-03-01T00:00:00Z date_updated: 2021-01-12T06:59:35Z day: '01' doi: 10.1007/s10955-012-0445-6 extern: 1 intvolume: ' 146' issue: '5' month: '03' page: 900 - 923 publication: Journal of Statistical Physics publication_status: published publisher: Springer publist_id: '4119' quality_controlled: 0 status: public title: Anderson localization at band edges for random magnetic fields type: journal_article volume: 146 year: '2012' ... --- _id: '2778' abstract: - lang: eng text: We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a "convexified measure" so that the local statistics are preserved under this convexification. author: - first_name: Paul full_name: Bourgade, Paul last_name: Bourgade - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau citation: ama: Bourgade P, Erdös L, Yau H. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.4751478 apa: Bourgade, P., Erdös, L., & Yau, H. (2012). Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4751478 chicago: Bourgade, Paul, László Erdös, and Horng Yau. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.4751478. ieee: P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles with non-convex potential,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012. ista: Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9). mla: Bourgade, Paul, et al. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute of Physics, 2012, doi:10.1063/1.4751478. short: P. Bourgade, L. Erdös, H. Yau, Journal of Mathematical Physics 53 (2012). date_created: 2018-12-11T11:59:33Z date_published: 2012-09-28T00:00:00Z date_updated: 2021-01-12T06:59:38Z day: '28' doi: 10.1063/1.4751478 extern: 1 intvolume: ' 53' issue: '9' month: '09' publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '4112' quality_controlled: 0 status: public title: Bulk universality of general β-ensembles with non-convex potential type: journal_article volume: 53 year: '2012' ... --- _id: '2779' abstract: - lang: eng text: We consider a two-dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate that does not rely on the monotonicity of the energy on the random parameters. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: David full_name: Hasler, David G last_name: Hasler citation: ama: Erdös L, Hasler D. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. 2012;13(8):1719-1731. doi:10.1007/s00023-012-0177-9 apa: Erdös, L., & Hasler, D. (2012). Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-012-0177-9 chicago: Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian on ℤ 2.” Annales Henri Poincare. Birkhäuser, 2012. https://doi.org/10.1007/s00023-012-0177-9. ieee: L. Erdös and D. Hasler, “Wegner estimate for random magnetic Laplacian on ℤ 2,” Annales Henri Poincare, vol. 13, no. 8. Birkhäuser, pp. 1719–1731, 2012. ista: Erdös L, Hasler D. 2012. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. 13(8), 1719–1731. mla: Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian on ℤ 2.” Annales Henri Poincare, vol. 13, no. 8, Birkhäuser, 2012, pp. 1719–31, doi:10.1007/s00023-012-0177-9. short: L. Erdös, D. Hasler, Annales Henri Poincare 13 (2012) 1719–1731. date_created: 2018-12-11T11:59:33Z date_published: 2012-12-01T00:00:00Z date_updated: 2021-01-12T06:59:38Z day: '01' doi: 10.1007/s00023-012-0177-9 extern: 1 intvolume: ' 13' issue: '8' month: '12' page: 1719 - 1731 publication: Annales Henri Poincare publication_status: published publisher: Birkhäuser publist_id: '4111' quality_controlled: 0 status: public title: Wegner estimate for random magnetic Laplacian on ℤ 2 type: journal_article volume: 13 year: '2012' ... --- _id: '2802' abstract: - lang: eng text: When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase-separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4-40 μm are detected and tracked. Based on these data, we resolve the oscillations in the droplet size distribution that are coupled to the convective flow. author: - first_name: Tobias full_name: Lapp, Tobias last_name: Lapp - first_name: Martin full_name: Rohloff, Martin last_name: Rohloff - first_name: Jürgen full_name: Vollmer, Jürgen T last_name: Vollmer - first_name: Björn full_name: Björn Hof id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 citation: ama: Lapp T, Rohloff M, Vollmer J, Hof B. Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. 2012;52(5):1187-1200. doi:10.1007/s00348-011-1243-7 apa: Lapp, T., Rohloff, M., Vollmer, J., & Hof, B. (2012). Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. Springer. https://doi.org/10.1007/s00348-011-1243-7 chicago: Lapp, Tobias, Martin Rohloff, Jürgen Vollmer, and Björn Hof. “Particle Tracking for Polydisperse Sedimenting Droplets in Phase Separation.” Experiments in Fluids. Springer, 2012. https://doi.org/10.1007/s00348-011-1243-7. ieee: T. Lapp, M. Rohloff, J. Vollmer, and B. Hof, “Particle tracking for polydisperse sedimenting droplets in phase separation,” Experiments in Fluids, vol. 52, no. 5. Springer, pp. 1187–1200, 2012. ista: Lapp T, Rohloff M, Vollmer J, Hof B. 2012. Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. 52(5), 1187–1200. mla: Lapp, Tobias, et al. “Particle Tracking for Polydisperse Sedimenting Droplets in Phase Separation.” Experiments in Fluids, vol. 52, no. 5, Springer, 2012, pp. 1187–200, doi:10.1007/s00348-011-1243-7. short: T. Lapp, M. Rohloff, J. Vollmer, B. Hof, Experiments in Fluids 52 (2012) 1187–1200. date_created: 2018-12-11T11:59:40Z date_published: 2012-05-05T00:00:00Z date_updated: 2021-01-12T06:59:49Z day: '05' doi: 10.1007/s00348-011-1243-7 extern: 1 intvolume: ' 52' issue: '5' month: '05' page: 1187 - 1200 publication: Experiments in Fluids publication_status: published publisher: Springer publist_id: '4087' quality_controlled: 0 status: public title: Particle tracking for polydisperse sedimenting droplets in phase separation type: journal_article volume: 52 year: '2012' ...