---
_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'
...