---
_id: '2776'
abstract:
- lang: eng
text: We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs,
i.e. graphs on N vertices where every edge is chosen independently and with probability
p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one.
Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions
both in the bulk and at the edge of the spectrum. More precisely, we prove (1)
that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum
has the same distribution as that of the Gaussian orthogonal ensemble; and (2)
that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution
as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application
of our method, we prove the bulk universality of generalized Wigner matrices under
the assumption that the matrix entries have at least 4 + ε moments.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Antti
full_name: Knowles, Antti
last_name: Knowles
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: 'Erdös L, Knowles A, Yau H, Yin J. Spectral statistics of Erdős-Rényi graphs
II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical
Physics. 2012;314(3):587-640. doi:10.1007/s00220-012-1527-7'
apa: 'Erdös, L., Knowles, A., Yau, H., & Yin, J. (2012). Spectral statistics
of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1527-7'
chicago: 'Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Spectral Statistics
of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues.” Communications
in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1527-7.'
ieee: 'L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi
graphs II: Eigenvalue spacing and the extreme eigenvalues,” Communications
in Mathematical Physics, vol. 314, no. 3. Springer, pp. 587–640, 2012.'
ista: 'Erdös L, Knowles A, Yau H, Yin J. 2012. Spectral statistics of Erdős-Rényi
graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical
Physics. 314(3), 587–640.'
mla: 'Erdös, László, et al. “Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue
Spacing and the Extreme Eigenvalues.” Communications in Mathematical Physics,
vol. 314, no. 3, Springer, 2012, pp. 587–640, doi:10.1007/s00220-012-1527-7.'
short: L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics
314 (2012) 587–640.
date_created: 2018-12-11T11:59:32Z
date_published: 2012-09-01T00:00:00Z
date_updated: 2021-01-12T06:59:37Z
day: '01'
doi: 10.1007/s00220-012-1527-7
extern: 1
intvolume: ' 314'
issue: '3'
month: '09'
page: 587 - 640
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4114'
quality_controlled: 0
status: public
title: 'Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme
eigenvalues'
type: journal_article
volume: 314
year: '2012'
...
---
_id: '2774'
abstract:
- lang: eng
text: We consider a large neutral molecule with total nuclear charge Z in non-relativistic
quantum mechanics with a self-generated classical electromagnetic field. To ensure
stability, we assume that Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes
the fine structure constant. We show that, in the simultaneous limit Z → ∞, α
→ 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given
by a two term expansion c 1Z 7/3 + c 2(κ) Z 2 + o(Z 2). The leading term is given
by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field
affects only the second (so-called Scott) term in the expansion.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Søren
full_name: Fournais, Søren
last_name: Fournais
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: Erdös L, Fournais S, Solovej J. Scott correction for large atoms and molecules
in a self-generated magnetic field. Communications in Mathematical Physics.
2012;312(3):847-882. doi:10.1007/s00220-012-1468-1
apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Scott correction for large
atoms and molecules in a self-generated magnetic field. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-012-1468-1
chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Scott Correction for Large
Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in
Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1468-1.
ieee: L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and
molecules in a self-generated magnetic field,” Communications in Mathematical
Physics, vol. 312, no. 3. Springer, pp. 847–882, 2012.
ista: Erdös L, Fournais S, Solovej J. 2012. Scott correction for large atoms and
molecules in a self-generated magnetic field. Communications in Mathematical Physics.
312(3), 847–882.
mla: Erdös, László, et al. “Scott Correction for Large Atoms and Molecules in a
Self-Generated Magnetic Field.” Communications in Mathematical Physics,
vol. 312, no. 3, Springer, 2012, pp. 847–82, doi:10.1007/s00220-012-1468-1.
short: L. Erdös, S. Fournais, J. Solovej, Communications in Mathematical Physics
312 (2012) 847–882.
date_created: 2018-12-11T11:59:31Z
date_published: 2012-06-01T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '01'
doi: 10.1007/s00220-012-1468-1
extern: 1
intvolume: ' 312'
issue: '3'
month: '06'
page: 847 - 882
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4116'
quality_controlled: 0
status: public
title: Scott correction for large atoms and molecules in a self-generated magnetic
field
type: journal_article
volume: 312
year: '2012'
...
---
_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'
...
---
_id: '2803'
abstract:
- lang: eng
text: Recent numerical studies suggest that in pipe and related shear flows, the
region of phase space separating laminar from turbulent motion is organized by
a chaotic attractor, called an edge state, which mediates the transition process.
We here confirm the existence of the edge state in laboratory experiments. We
observe that it governs the dynamics during the decay of turbulence underlining
its potential relevance for turbulence control. In addition we unveil two unstable
traveling wave solutions underlying the experimental flow fields. This observation
corroborates earlier suggestions that unstable solutions organize turbulence and
its stability border.
author:
- first_name: Alberto
full_name: de Lózar, Alberto
last_name: De Lózar
- first_name: Fernando
full_name: Mellibovsky, Fernando
last_name: Mellibovsky
- first_name: Marc
full_name: Avila, Marc
last_name: Avila
- first_name: Björn
full_name: Björn Hof
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: De Lózar A, Mellibovsky F, Avila M, Hof B. Edge state in pipe flow experiments.
Physical Review Letters. 2012;108(21). doi:10.1103/PhysRevLett.108.214502
apa: De Lózar, A., Mellibovsky, F., Avila, M., & Hof, B. (2012). Edge state
in pipe flow experiments. Physical Review Letters. American Physical Society.
https://doi.org/10.1103/PhysRevLett.108.214502
chicago: De Lózar, Alberto, Fernando Mellibovsky, Marc Avila, and Björn Hof. “Edge
State in Pipe Flow Experiments.” Physical Review Letters. American Physical
Society, 2012. https://doi.org/10.1103/PhysRevLett.108.214502.
ieee: A. De Lózar, F. Mellibovsky, M. Avila, and B. Hof, “Edge state in pipe flow
experiments,” Physical Review Letters, vol. 108, no. 21. American Physical
Society, 2012.
ista: De Lózar A, Mellibovsky F, Avila M, Hof B. 2012. Edge state in pipe flow experiments.
Physical Review Letters. 108(21).
mla: De Lózar, Alberto, et al. “Edge State in Pipe Flow Experiments.” Physical
Review Letters, vol. 108, no. 21, American Physical Society, 2012, doi:10.1103/PhysRevLett.108.214502.
short: A. De Lózar, F. Mellibovsky, M. Avila, B. Hof, Physical Review Letters 108
(2012).
date_created: 2018-12-11T11:59:41Z
date_published: 2012-05-21T00:00:00Z
date_updated: 2021-01-12T06:59:49Z
day: '21'
doi: 10.1103/PhysRevLett.108.214502
extern: 1
intvolume: ' 108'
issue: '21'
month: '05'
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4086'
quality_controlled: 0
status: public
title: Edge state in pipe flow experiments
type: journal_article
volume: 108
year: '2012'
...
---
_id: '2804'
abstract:
- lang: eng
text: The analysis of the size distribution of droplets condensing on a substrate
(breath figures) is a test ground for scaling theories. Here, we show that a faithful
description of these distributions must explicitly deal with the growth mechanisms
of the droplets. This finding establishes a gateway connecting nucleation and
growth of the smallest droplets on surfaces to gross features of the evolution
of the droplet size distribution
author:
- first_name: Johannes
full_name: Blaschke, Johannes
last_name: Blaschke
- first_name: Tobias
full_name: Lapp, Tobias
last_name: Lapp
- first_name: Björn
full_name: Björn Hof
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
- first_name: Jürgen
full_name: Vollmer, Jürgen T
last_name: Vollmer
citation:
ama: 'Blaschke J, Lapp T, Hof B, Vollmer J. Breath figures: Nucleation, growth,
coalescence, and the size distribution of droplets. Physical Review Letters.
2012;109(6). doi:10.1103/PhysRevLett.109.068701'
apa: 'Blaschke, J., Lapp, T., Hof, B., & Vollmer, J. (2012). Breath figures:
Nucleation, growth, coalescence, and the size distribution of droplets. Physical
Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.109.068701'
chicago: 'Blaschke, Johannes, Tobias Lapp, Björn Hof, and Jürgen Vollmer. “Breath
Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets.”
Physical Review Letters. American Physical Society, 2012. https://doi.org/10.1103/PhysRevLett.109.068701.'
ieee: 'J. Blaschke, T. Lapp, B. Hof, and J. Vollmer, “Breath figures: Nucleation,
growth, coalescence, and the size distribution of droplets,” Physical Review
Letters, vol. 109, no. 6. American Physical Society, 2012.'
ista: 'Blaschke J, Lapp T, Hof B, Vollmer J. 2012. Breath figures: Nucleation, growth,
coalescence, and the size distribution of droplets. Physical Review Letters. 109(6).'
mla: 'Blaschke, Johannes, et al. “Breath Figures: Nucleation, Growth, Coalescence,
and the Size Distribution of Droplets.” Physical Review Letters, vol. 109,
no. 6, American Physical Society, 2012, doi:10.1103/PhysRevLett.109.068701.'
short: J. Blaschke, T. Lapp, B. Hof, J. Vollmer, Physical Review Letters 109 (2012).
date_created: 2018-12-11T11:59:41Z
date_published: 2012-08-10T00:00:00Z
date_updated: 2021-01-12T06:59:50Z
day: '10'
doi: 10.1103/PhysRevLett.109.068701
extern: 1
intvolume: ' 109'
issue: '6'
month: '08'
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4085'
quality_controlled: 0
status: public
title: 'Breath figures: Nucleation, growth, coalescence, and the size distribution
of droplets'
type: journal_article
volume: 109
year: '2012'
...
---
_id: '2825'
abstract:
- lang: eng
text: 'We study the problem of maximum marginal prediction (MMP) in probabilistic
graphical models, a task that occurs, for example, as the Bayes optimal decision
rule under a Hamming loss. MMP is typically performed as a two-stage procedure:
one estimates each variable''s marginal probability and then forms a prediction
from the states of maximal probability. In this work we propose a simple yet effective
technique for accelerating MMP when inference is sampling-based: instead of the
above two-stage procedure we directly estimate the posterior probability of each
decision variable. This allows us to identify the point of time when we are sufficiently
certain about any individual decision. Whenever this is the case, we dynamically
prune the variables we are confident about from the underlying factor graph. Consequently,
at any time only samples of variables whose decision is still uncertain need to
be created. Experiments in two prototypical scenarios, multi-label classification
and image inpainting, show that adaptive sampling can drastically accelerate MMP
without sacrificing prediction accuracy.'
author:
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Lampert C. Dynamic pruning of factor graphs for maximum marginal prediction.
In: Vol 1. Neural Information Processing Systems; 2012:82-90.'
apa: 'Lampert, C. (2012). Dynamic pruning of factor graphs for maximum marginal
prediction (Vol. 1, pp. 82–90). Presented at the NIPS: Neural Information Processing
Systems, Lake Tahoe, NV, United States: Neural Information Processing Systems.'
chicago: Lampert, Christoph. “Dynamic Pruning of Factor Graphs for Maximum Marginal
Prediction,” 1:82–90. Neural Information Processing Systems, 2012.
ieee: 'C. Lampert, “Dynamic pruning of factor graphs for maximum marginal prediction,”
presented at the NIPS: Neural Information Processing Systems, Lake Tahoe, NV,
United States, 2012, vol. 1, pp. 82–90.'
ista: 'Lampert C. 2012. Dynamic pruning of factor graphs for maximum marginal prediction.
NIPS: Neural Information Processing Systems vol. 1, 82–90.'
mla: Lampert, Christoph. Dynamic Pruning of Factor Graphs for Maximum Marginal
Prediction. Vol. 1, Neural Information Processing Systems, 2012, pp. 82–90.
short: C. Lampert, in:, Neural Information Processing Systems, 2012, pp. 82–90.
conference:
end_date: 2012-12-06
location: Lake Tahoe, NV, United States
name: 'NIPS: Neural Information Processing Systems'
start_date: 2012-12-03
date_created: 2018-12-11T11:59:48Z
date_published: 2012-12-01T00:00:00Z
date_updated: 2021-01-12T06:59:59Z
day: '01'
department:
- _id: ChLa
intvolume: ' 1'
language:
- iso: eng
month: '12'
oa_version: None
page: 82 - 90
publication_status: published
publisher: Neural Information Processing Systems
publist_id: '3975'
quality_controlled: '1'
scopus_import: 1
status: public
title: Dynamic pruning of factor graphs for maximum marginal prediction
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2012'
...