---
_id: '2768'
abstract:
- lang: eng
text: We consider a two dimensional magnetic Schrödinger operator with a spatially
stationary random magnetic field. We assume that the magnetic field has a positive
lower bound and that it has Fourier modes on arbitrarily short scales. We prove
the Wegner estimate at arbitrary energy, i. e. we show that the averaged density
of states is finite throughout the whole spectrum. We also prove Anderson localization
at the bottom of the spectrum.
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 and Anderson localization for random magnetic
fields. Communications in Mathematical Physics. 2012;309(2):507-542. doi:10.1007/s00220-011-1373-z
apa: Erdös, L., & Hasler, D. (2012). Wegner estimate and Anderson localization
for random magnetic fields. Communications in Mathematical Physics. Springer.
https://doi.org/10.1007/s00220-011-1373-z
chicago: Erdös, László, and David Hasler. “Wegner Estimate and Anderson Localization
for Random Magnetic Fields.” Communications in Mathematical Physics. Springer,
2012. https://doi.org/10.1007/s00220-011-1373-z.
ieee: L. Erdös and D. Hasler, “Wegner estimate and Anderson localization for random
magnetic fields,” Communications in Mathematical Physics, vol. 309, no.
2. Springer, pp. 507–542, 2012.
ista: Erdös L, Hasler D. 2012. Wegner estimate and Anderson localization for random
magnetic fields. Communications in Mathematical Physics. 309(2), 507–542.
mla: Erdös, László, and David Hasler. “Wegner Estimate and Anderson Localization
for Random Magnetic Fields.” Communications in Mathematical Physics, vol.
309, no. 2, Springer, 2012, pp. 507–42, doi:10.1007/s00220-011-1373-z.
short: L. Erdös, D. Hasler, Communications in Mathematical Physics 309 (2012) 507–542.
date_created: 2018-12-11T11:59:30Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2021-01-12T06:59:34Z
day: '01'
doi: 10.1007/s00220-011-1373-z
extern: 1
fulldoi: https://doi.org/10.1007/s00220-011-1373-z
intvolume: ' 309'
issue: '2'
month: '01'
page: 507 - 542
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4122'
quality_controlled: 0
status: public
title: Wegner estimate and Anderson localization for random magnetic fields
type: journal_article
volume: 309
year: '2012'
...
---
_id: '2769'
abstract:
- lang: eng
text: We present a generalization of the method of the local relaxation flow to
establish the universality of local spectral statistics of a broad class of large
random matrices. We show that the local distribution of the eigenvalues coincides
with the local statistics of the corresponding Gaussian ensemble provided the
distribution of the individual matrix element is smooth and the eigenvalues {X
J} N j=1 are close to their classical location {y j} N j=1 determined by the limiting
density of eigenvalues. Under the scaling where the typical distance between neighboring
eigenvalues is of order 1/N, the necessary apriori estimate on the location of
eigenvalues requires only to know that E|x j - γ j| 2 ≤ N-1-ε on average. This
information can be obtained by well established methods for various matrix ensembles.
We demonstrate the method by proving local spectral universality for sample covariance
matrices.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- 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, Schlein B, Yau H, Yin J. The local relaxation flow approach to universality
of the local statistics for random matrices. Annales de l’institut Henri Poincare
(B) Probability and Statistics. 2012;48(1):1-46. doi:10.1214/10-AIHP388
apa: Erdös, L., Schlein, B., Yau, H., & Yin, J. (2012). The local relaxation
flow approach to universality of the local statistics for random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. Institute of
Mathematical Statistics. https://doi.org/10.1214/10-AIHP388
chicago: Erdös, László, Benjamin Schlein, Horng Yau, and Jun Yin. “The Local Relaxation
Flow Approach to Universality of the Local Statistics for Random Matrices.” Annales
de l’institut Henri Poincare (B) Probability and Statistics. Institute of
Mathematical Statistics, 2012. https://doi.org/10.1214/10-AIHP388.
ieee: L. Erdös, B. Schlein, H. Yau, and J. Yin, “The local relaxation flow approach
to universality of the local statistics for random matrices,” Annales de l’institut
Henri Poincare (B) Probability and Statistics, vol. 48, no. 1. Institute of
Mathematical Statistics, pp. 1–46, 2012.
ista: Erdös L, Schlein B, Yau H, Yin J. 2012. The local relaxation flow approach
to universality of the local statistics for random matrices. Annales de l’institut
Henri Poincare (B) Probability and Statistics. 48(1), 1–46.
mla: Erdös, László, et al. “The Local Relaxation Flow Approach to Universality of
the Local Statistics for Random Matrices.” Annales de l’institut Henri Poincare
(B) Probability and Statistics, vol. 48, no. 1, Institute of Mathematical
Statistics, 2012, pp. 1–46, doi:10.1214/10-AIHP388.
short: L. Erdös, B. Schlein, H. Yau, J. Yin, Annales de l’institut Henri Poincare
(B) Probability and Statistics 48 (2012) 1–46.
date_created: 2018-12-11T11:59:30Z
date_published: 2012-02-01T00:00:00Z
date_updated: 2021-01-12T06:59:34Z
day: '01'
doi: 10.1214/10-AIHP388
extern: 1
fulldoi: https://doi.org/10.1214/10-AIHP388
intvolume: ' 48'
issue: '1'
month: '02'
page: 1 - 46
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '4121'
quality_controlled: 0
status: public
title: The local relaxation flow approach to universality of the local statistics
for random matrices
type: journal_article
volume: 48
year: '2012'
...
---
_id: '2770'
abstract:
- lang: eng
text: 'Consider N×N Hermitian or symmetric random matrices H with independent entries,
where the distribution of the (i,j) matrix element is given by the probability
measure vij with zero expectation and with variance σ ιj 2. We assume that the
variances satisfy the normalization condition Σiσij2=1 for all j and that there
is a positive constant c such that c≤Nσ ιj 2 ιc -1. We further assume that the
probability distributions νij have a uniform subexponential decay. We prove that
the Stieltjes transform of the empirical eigenvalue distribution of H is given
by the Wigner semicircle law uniformly up to the edges of the spectrum with an
error of order (Nη) -1 where η is the imaginary part of the spectral parameter
in the Stieltjes transform. There are three corollaries to this strong local semicircle
law: (1) Rigidity of eigenvalues: If γj=γj,N denotes the classical location of
the j-th eigenvalue under the semicircle law ordered in increasing order, then
the j-th eigenvalue λj is close to γj in the sense that for some positive constants
C, c P{double-struck}(∃j:|λ j-γ j|≥(logN) CloglogN[min(j,N-j+1)] -1/3N -2/3)≤
C exp[-(logN) cloglogN] for N large enough. (2) The proof of Dyson''s conjecture
(Dyson, 1962 [15]) which states that the time scale of the Dyson Brownian motion
to reach local equilibrium is of order N -1 up to logarithmic corrections. (3)
The edge universality holds in the sense that the probability distributions of
the largest (and the smallest) eigenvalues of two generalized Wigner ensembles
are the same in the large N limit provided that the second moments of the two
ensembles are identical.'
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
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Erdös L, Yau H, Yin J. Rigidity of eigenvalues of generalized Wigner matrices.
Advances in Mathematics. 2012;229(3):1435-1515. doi:10.1016/j.aim.2011.12.010
apa: Erdös, L., Yau, H., & Yin, J. (2012). Rigidity of eigenvalues of generalized
Wigner matrices. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2011.12.010
chicago: Erdös, László, Horng Yau, and Jun Yin. “Rigidity of Eigenvalues of Generalized
Wigner Matrices.” Advances in Mathematics. Academic Press, 2012. https://doi.org/10.1016/j.aim.2011.12.010.
ieee: L. Erdös, H. Yau, and J. Yin, “Rigidity of eigenvalues of generalized Wigner
matrices,” Advances in Mathematics, vol. 229, no. 3. Academic Press, pp.
1435–1515, 2012.
ista: Erdös L, Yau H, Yin J. 2012. Rigidity of eigenvalues of generalized Wigner
matrices. Advances in Mathematics. 229(3), 1435–1515.
mla: Erdös, László, et al. “Rigidity of Eigenvalues of Generalized Wigner Matrices.”
Advances in Mathematics, vol. 229, no. 3, Academic Press, 2012, pp. 1435–515,
doi:10.1016/j.aim.2011.12.010.
short: L. Erdös, H. Yau, J. Yin, Advances in Mathematics 229 (2012) 1435–1515.
date_created: 2018-12-11T11:59:30Z
date_published: 2012-02-15T00:00:00Z
date_updated: 2021-01-12T06:59:35Z
day: '15'
doi: 10.1016/j.aim.2011.12.010
extern: 1
fulldoi: https://doi.org/10.1016/j.aim.2011.12.010
intvolume: ' 229'
issue: '3'
month: '02'
page: 1435 - 1515
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '4120'
quality_controlled: 0
status: public
title: Rigidity of eigenvalues of generalized Wigner matrices
type: journal_article
volume: 229
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
fulldoi: https://doi.org/10.1007/s10955-012-0445-6
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: '2772'
abstract:
- lang: eng
text: We consider the semiclassical asymptotics of the sum of negative eigenvalues
of the three-dimensional Pauli operator with an external potential and a self-generated
magnetic field B. We also add the field energy β ∫ B 2 and we minimize over all
magnetic fields. The parameter β effectively determines the strength of the field.
We consider the weak field regime with βh 2 ≥ const > 0, where h is the semiclassical
parameter. For smooth potentials we prove that the semiclassical asymptotics of
the total energy is given by the non-magnetic Weyl term to leading order with
an error bound that is smaller by a factor h 1+e{open}, i. e. the subleading term
vanishes. However for potentials with a Coulomb singularity, the subleading term
does not vanish due to the non-semiclassical effect of the singularity. Combined
with a multiscale technique, this refined estimate is used in the companion paper
(Erdo{double acute}s et al. in Scott correction for large molecules with a self-generated
magnetic field, Preprint, 2011) to prove the second order Scott correction to
the ground state energy of large atoms and molecules.
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. Second order semiclassics with self generated
magnetic fields. Annales Henri Poincare. 2012;13(4):671-730. doi:10.1007/s00023-011-0150-z
apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Second order semiclassics
with self generated magnetic fields. Annales Henri Poincare. Birkhäuser.
https://doi.org/10.1007/s00023-011-0150-z
chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Second Order Semiclassics
with Self Generated Magnetic Fields.” Annales Henri Poincare. Birkhäuser,
2012. https://doi.org/10.1007/s00023-011-0150-z.
ieee: L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self
generated magnetic fields,” Annales Henri Poincare, vol. 13, no. 4. Birkhäuser,
pp. 671–730, 2012.
ista: Erdös L, Fournais S, Solovej J. 2012. Second order semiclassics with self
generated magnetic fields. Annales Henri Poincare. 13(4), 671–730.
mla: Erdös, László, et al. “Second Order Semiclassics with Self Generated Magnetic
Fields.” Annales Henri Poincare, vol. 13, no. 4, Birkhäuser, 2012, pp.
671–730, doi:10.1007/s00023-011-0150-z.
short: L. Erdös, S. Fournais, J. Solovej, Annales Henri Poincare 13 (2012) 671–730.
date_created: 2018-12-11T11:59:31Z
date_published: 2012-05-01T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '01'
doi: 10.1007/s00023-011-0150-z
extern: 1
fulldoi: https://doi.org/10.1007/s00023-011-0150-z
intvolume: ' 13'
issue: '4'
month: '05'
page: 671 - 730
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '4118'
quality_controlled: 0
status: public
title: Second order semiclassics with self generated magnetic fields
type: journal_article
volume: 13
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
fulldoi: https://doi.org/10.1214/EJP.v17-1779
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: '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
fulldoi: https://doi.org/10.1007/s00220-012-1468-1
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: '2775'
abstract:
- lang: eng
text: The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue
statistics of large random matrices exhibit universal behavior depending only
on the symmetry class of the matrix ensemble. For invariant matrix models, the
eigenvalue distributions are given by a log-gas with potential V and inverse temperature
β = 1, 2, 4, corresponding to the orthogonal, unitary and symplectic ensembles.
For β ∉ {1, 2, 4}, there is no natural random matrix ensemble behind this model,
but the statistical physics interpretation of the log-gas is still valid for all
β > 0. The universality conjecture for invariant ensembles asserts that the
local eigenvalue statistics are independent of V. In this article, we review our
recent solution to the universality conjecture for both invariant and non-invariant
ensembles. We will also demonstrate that the local ergodicity of the Dyson Brownian
motion is the intrinsic mechanism behind the universality. Furthermore, we review
the solution of Dyson's conjecture on the local relaxation time of the Dyson Brownian
motion. Related questions such as delocalization of eigenvectors and local version
of Wigner's semicircle law will also be discussed.
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. Universality of local spectral statistics of random matrices.
Bulletin of the American Mathematical Society. 2012;49(3):377-414. doi:10.1090/S0273-0979-2012-01372-1
apa: Erdös, L., & Yau, H. (2012). Universality of local spectral statistics
of random matrices. Bulletin of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/S0273-0979-2012-01372-1
chicago: Erdös, László, and Horng Yau. “Universality of Local Spectral Statistics
of Random Matrices.” Bulletin of the American Mathematical Society. American
Mathematical Society, 2012. https://doi.org/10.1090/S0273-0979-2012-01372-1.
ieee: L. Erdös and H. Yau, “Universality of local spectral statistics of random
matrices,” Bulletin of the American Mathematical Society, vol. 49, no.
3. American Mathematical Society, pp. 377–414, 2012.
ista: Erdös L, Yau H. 2012. Universality of local spectral statistics of random
matrices. Bulletin of the American Mathematical Society. 49(3), 377–414.
mla: Erdös, László, and Horng Yau. “Universality of Local Spectral Statistics of
Random Matrices.” Bulletin of the American Mathematical Society, vol. 49,
no. 3, American Mathematical Society, 2012, pp. 377–414, doi:10.1090/S0273-0979-2012-01372-1.
short: L. Erdös, H. Yau, Bulletin of the American Mathematical Society 49 (2012)
377–414.
date_created: 2018-12-11T11:59:32Z
date_published: 2012-01-30T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '30'
doi: 10.1090/S0273-0979-2012-01372-1
extern: 1
fulldoi: https://doi.org/10.1090/S0273-0979-2012-01372-1
intvolume: ' 49'
issue: '3'
month: '01'
page: 377 - 414
publication: Bulletin of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '4115'
quality_controlled: 0
status: public
title: Universality of local spectral statistics of random matrices
type: journal_article
volume: 49
year: '2012'
...
---
_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
fulldoi: https://doi.org/10.1007/s00220-012-1527-7
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: '2777'
abstract:
- lang: eng
text: We consider a large neutral molecule with total nuclear charge Z in a model
with self-generated classical magnetic field and where the kinetic energy of the
electrons is treated relativistically. To ensure stability, we assume that Zα
< 2/π, where α denotes the fine structure constant. We are interested in the
ground state energy in the simultaneous limit Z → ∞, α → 0 such that κ = Zα is
fixed. The leading term in the energy asymptotics is independent of κ, it is given
by the Thomas-Fermi energy of order Z7/3 and it is unchanged by including the
self-generated magnetic field. We prove the first correction term to this energy,
the so-called Scott correction of the form S(αZ)Z2. The current paper extends
the result of Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)] on
the Scott correction for relativistic molecules to include a self-generated magnetic
field. Furthermore, we show that the corresponding Scott correction function S,
first identified by Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)],
is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities
for the relativistic kinetic energy with magnetic fields.
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. Relativistic Scott correction in self-generated
magnetic fields. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.3697417
apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Relativistic Scott correction
in self-generated magnetic fields. Journal of Mathematical Physics. American
Institute of Physics. https://doi.org/10.1063/1.3697417
chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Relativistic Scott Correction
in Self-Generated Magnetic Fields.” Journal of Mathematical Physics. American
Institute of Physics, 2012. https://doi.org/10.1063/1.3697417.
ieee: L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated
magnetic fields,” Journal of Mathematical Physics, vol. 53, no. 9. American
Institute of Physics, 2012.
ista: Erdös L, Fournais S, Solovej J. 2012. Relativistic Scott correction in self-generated
magnetic fields. Journal of Mathematical Physics. 53(9).
mla: Erdös, László, et al. “Relativistic Scott Correction in Self-Generated Magnetic
Fields.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute
of Physics, 2012, doi:10.1063/1.3697417.
short: L. Erdös, S. Fournais, J. Solovej, Journal of Mathematical Physics 53 (2012).
date_created: 2018-12-11T11:59:32Z
date_published: 2012-09-28T00:00:00Z
date_updated: 2021-01-12T06:59:37Z
day: '28'
doi: 10.1063/1.3697417
extern: 1
fulldoi: https://doi.org/10.1063/1.3697417
intvolume: ' 53'
issue: '9'
month: '09'
publication: Journal of Mathematical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '4113'
quality_controlled: 0
status: public
title: Relativistic Scott correction in self-generated magnetic fields
type: journal_article
volume: 53
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
fulldoi: https://doi.org/10.1063/1.4751478
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
fulldoi: https://doi.org/10.1007/s00023-012-0177-9
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
fulldoi: https://doi.org/10.1007/s00348-011-1243-7
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
fulldoi: https://doi.org/10.1103/PhysRevLett.108.214502
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
fulldoi: https://doi.org/10.1103/PhysRevLett.109.068701
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.'
article_processing_charge: No
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 Foundation; 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
Foundation.'
chicago: Lampert, Christoph. “Dynamic Pruning of Factor Graphs for Maximum Marginal
Prediction,” 1:82–90. Neural Information Processing Systems Foundation, 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 Foundation, 2012,
pp. 82–90.
short: C. Lampert, in:, Neural Information Processing Systems Foundation, 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
corr_author: '1'
date_created: 2018-12-11T11:59:48Z
date_published: 2012-12-01T00:00:00Z
date_updated: 2025-06-03T11:46:36Z
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 Foundation
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2012'
...
---
_id: '2848'
abstract:
- lang: eng
text: We study evolutionary game theory in a setting where individuals learn from
each other. We extend the traditional approach by assuming that a population contains
individuals with different learning abilities. In particular, we explore the situation
where individuals have different search spaces, when attempting to learn the strategies
of others. The search space of an individual specifies the set of strategies learnable
by that individual. The search space is genetically given and does not change
under social evolutionary dynamics. We introduce a general framework and study
a specific example in the context of direct reciprocity. For this example, we
obtain the counter intuitive result that cooperation can only evolve for intermediate
benefit-to-cost ratios, while small and large benefit-to-cost ratios favor defection.
Our paper is a step toward making a connection between computational learning
theory and evolutionary game dynamics.
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Damien
full_name: Zufferey, Damien
id: 4397AC76-F248-11E8-B48F-1D18A9856A87
last_name: Zufferey
orcid: 0000-0002-3197-8736
- first_name: Martin
full_name: Nowak, Martin
last_name: Nowak
citation:
ama: Chatterjee K, Zufferey D, Nowak M. Evolutionary game dynamics in populations
with different learners. Journal of Theoretical Biology. 2012;301:161-173.
doi:10.1016/j.jtbi.2012.02.021
apa: Chatterjee, K., Zufferey, D., & Nowak, M. (2012). Evolutionary game dynamics
in populations with different learners. Journal of Theoretical Biology.
Elsevier. https://doi.org/10.1016/j.jtbi.2012.02.021
chicago: Chatterjee, Krishnendu, Damien Zufferey, and Martin Nowak. “Evolutionary
Game Dynamics in Populations with Different Learners.” Journal of Theoretical
Biology. Elsevier, 2012. https://doi.org/10.1016/j.jtbi.2012.02.021.
ieee: K. Chatterjee, D. Zufferey, and M. Nowak, “Evolutionary game dynamics in populations
with different learners,” Journal of Theoretical Biology, vol. 301. Elsevier,
pp. 161–173, 2012.
ista: Chatterjee K, Zufferey D, Nowak M. 2012. Evolutionary game dynamics in populations
with different learners. Journal of Theoretical Biology. 301, 161–173.
mla: Chatterjee, Krishnendu, et al. “Evolutionary Game Dynamics in Populations with
Different Learners.” Journal of Theoretical Biology, vol. 301, Elsevier,
2012, pp. 161–73, doi:10.1016/j.jtbi.2012.02.021.
short: K. Chatterjee, D. Zufferey, M. Nowak, Journal of Theoretical Biology 301
(2012) 161–173.
corr_author: '1'
date_created: 2018-12-11T11:59:55Z
date_published: 2012-05-21T00:00:00Z
date_updated: 2025-09-30T08:20:22Z
day: '21'
department:
- _id: KrCh
- _id: ToHe
doi: 10.1016/j.jtbi.2012.02.021
ec_funded: 1
external_id:
isi:
- '000303079500016'
pmid:
- '22394652'
fulldoi: https://doi.org/10.1016/j.jtbi.2012.02.021
intvolume: ' 301'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3322297/
month: '05'
oa: 1
oa_version: Submitted Version
page: 161 - 173
pmid: 1
project:
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication: Journal of Theoretical Biology
publication_status: published
publisher: Elsevier
publist_id: '3946'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Evolutionary game dynamics in populations with different learners
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 301
year: '2012'
...
---
_id: '2849'
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Nataliya
full_name: Strelkova, Nataliya
last_name: Strelkova
citation:
ama: Edelsbrunner H, Strelkova N. On the configuration space of Steiner minimal
trees. Russian Mathematical Surveys. 2012;67(6):1167-1168. doi:10.1070/RM2012v067n06ABEH004820
apa: Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space of
Steiner minimal trees. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM2012v067n06ABEH004820
chicago: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
of Steiner Minimal Trees.” Russian Mathematical Surveys. IOP Publishing,
2012. https://doi.org/10.1070/RM2012v067n06ABEH004820.
ieee: H. Edelsbrunner and N. Strelkova, “On the configuration space of Steiner minimal
trees,” Russian Mathematical Surveys, vol. 67, no. 6. IOP Publishing, pp.
1167–1168, 2012.
ista: Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal
trees. Russian Mathematical Surveys. 67(6), 1167–1168.
mla: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space
of Steiner Minimal Trees.” Russian Mathematical Surveys, vol. 67, no. 6,
IOP Publishing, 2012, pp. 1167–68, doi:10.1070/RM2012v067n06ABEH004820.
short: H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168.
date_created: 2018-12-11T11:59:55Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2025-09-30T08:19:37Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1070/RM2012v067n06ABEH004820
external_id:
isi:
- '000315950100005'
file:
- access_level: open_access
checksum: 44ee8d173487e8ed41a51136816bbeb4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:26Z
date_updated: 2020-07-14T12:45:51Z
file_id: '5078'
file_name: IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf
file_size: 392021
relation: main_file
file_date_updated: 2020-07-14T12:45:51Z
fulldoi: https://doi.org/10.1070/RM2012v067n06ABEH004820
has_accepted_license: '1'
intvolume: ' 67'
isi: 1
issue: '6'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 1167 - 1168
publication: Russian Mathematical Surveys
publication_status: published
publisher: IOP Publishing
publist_id: '3943'
pubrep_id: '546'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the configuration space of Steiner minimal trees
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 67
year: '2012'
...
---
_id: '2875'
abstract:
- lang: eng
text: Phytohormones are important plant growth regulators that control many developmental
processes, such as cell division, cell differentiation, organogenesis and morphogenesis.
They regulate a multitude of apparently unrelated physiological processes, often
with overlapping roles, and they mutually modulate their effects. These features
imply important synergistic and antagonistic interactions between the various
plant hormones. Auxin and cytokinin are central hormones involved in the regulation
of plant growth and development, including processes determining root architecture,
such as root pole establishment during early embryogenesis, root meristem maintenance
and lateral root organogenesis. Thus, to control root development both pathways
put special demands on the mechanisms that balance their activities and mediate
their interactions. Here, we summarize recent knowledge on the role of auxin and
cytokinin in the regulation of root architecture with special focus on lateral
root organogenesis, discuss the latest findings on the molecular mechanisms of
their interactions, and present forward genetic screen as a tool to identify novel
molecular components of the auxin and cytokinin crosstalk.
author:
- first_name: Agnieszka
full_name: Bielach, Agnieszka
last_name: Bielach
- first_name: Jérôme
full_name: Duclercq, Jérôme
last_name: Duclercq
- first_name: Peter
full_name: Peter Marhavy
id: 3F45B078-F248-11E8-B48F-1D18A9856A87
last_name: Marhavy
orcid: 0000-0001-5227-5741
- first_name: Eva
full_name: Eva Benková
id: 38F4F166-F248-11E8-B48F-1D18A9856A87
last_name: Benková
orcid: 0000-0002-8510-9739
citation:
ama: Bielach A, Duclercq J, Marhavý P, Benková E. Genetic approach towards the identification
of auxin - cytokinin crosstalk components involved in root development. Philosophical
Transactions of the Royal Society of London Series B, Biological Sciences.
2012;367(1595):1469-1478. doi:10.1098/rstb.2011.0233
apa: Bielach, A., Duclercq, J., Marhavý, P., & Benková, E. (2012). Genetic approach
towards the identification of auxin - cytokinin crosstalk components involved
in root development. Philosophical Transactions of the Royal Society of London.
Series B, Biological Sciences. Royal Society, The. https://doi.org/10.1098/rstb.2011.0233
chicago: Bielach, Agnieszka, Jérôme Duclercq, Peter Marhavý, and Eva Benková. “Genetic
Approach towards the Identification of Auxin - Cytokinin Crosstalk Components
Involved in Root Development.” Philosophical Transactions of the Royal Society
of London. Series B, Biological Sciences. Royal Society, The, 2012. https://doi.org/10.1098/rstb.2011.0233.
ieee: A. Bielach, J. Duclercq, P. Marhavý, and E. Benková, “Genetic approach towards
the identification of auxin - cytokinin crosstalk components involved in root
development,” Philosophical Transactions of the Royal Society of London. Series
B, Biological Sciences, vol. 367, no. 1595. Royal Society, The, pp. 1469–1478,
2012.
ista: Bielach A, Duclercq J, Marhavý P, Benková E. 2012. Genetic approach towards
the identification of auxin - cytokinin crosstalk components involved in root
development. Philosophical Transactions of the Royal Society of London. Series
B, Biological Sciences. 367(1595), 1469–1478.
mla: Bielach, Agnieszka, et al. “Genetic Approach towards the Identification of
Auxin - Cytokinin Crosstalk Components Involved in Root Development.” Philosophical
Transactions of the Royal Society of London. Series B, Biological Sciences,
vol. 367, no. 1595, Royal Society, The, 2012, pp. 1469–78, doi:10.1098/rstb.2011.0233.
short: A. Bielach, J. Duclercq, P. Marhavý, E. Benková, Philosophical Transactions
of the Royal Society of London. Series B, Biological Sciences 367 (2012) 1469–1478.
date_created: 2018-12-11T12:00:05Z
date_published: 2012-06-05T00:00:00Z
date_updated: 2021-01-12T07:00:25Z
day: '05'
doi: 10.1098/rstb.2011.0233
extern: 1
fulldoi: https://doi.org/10.1098/rstb.2011.0233
intvolume: ' 367'
issue: '1595'
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3321684/
month: '06'
oa: 1
page: 1469 - 1478
publication: Philosophical Transactions of the Royal Society of London. Series B,
Biological Sciences
publication_status: published
publisher: Royal Society, The
publist_id: '3887'
quality_controlled: 0
status: public
title: Genetic approach towards the identification of auxin - cytokinin crosstalk
components involved in root development
type: journal_article
volume: 367
year: '2012'
...
---
_id: '2876'
abstract:
- lang: eng
text: Cytokinin (CK) activity is regulated by the complex interplay of their metabolism,
transport, stability and cellular/tissue localization. O-glucosides of zeatin-type
CKs are postulated to be storage and/or transport forms. Active CK levels are
determined in part by their differential distribution of CK metabolites across
different subcellular compartments. We have previously shown that overexpressing
chloroplast-localized Zm-p60.1, a maize β-glucosidase capable of releasing active
cytokinins from their O- and N3-glucosides, perturbs CK homeostasis in transgenic
tobacco. We obtained tobacco (Nicotiana tabacum L., cv Petit Havana SR1) plants
overexpressing a recombinant Zm-p60.1 that is targeted to the vacuole. The protein
is correctly processed and localized to the vacuole. When grown on medium containing
exogenous zeatin, transgenic seedlings rapidly accumulate fresh weight due to
ectopic growths at the base of the hypocotyl. The presence of the enzyme in these
ectopic structures is shown by histochemical staining. CK quantification reveals
that these transgenic seedlings are unable to accumulate zeatin-O-glucoside to
levels similar to those observed in the wild type. When crossed with tobacco overexpressing
the zeatin-O-glucosyltransferase gene from Phaseolus, the vacuolar variant shows
an almost complete reversion in the root elongation assay. This is the first evidence
from intact plants that the vacuole is the storage organelle for CK O-glucosides
and that they are available to attack by Zm-p60.1. We propose the use of Zm-p60.1
as a robust molecular tool that exploits the reversibility of O-glucosylation
and enables delicate manipulations of active CK content at the cellular level.
author:
- first_name: Nagavalli
full_name: Kiran, Nagavalli S
last_name: Kiran
- first_name: Eva
full_name: Eva Benková
id: 38F4F166-F248-11E8-B48F-1D18A9856A87
last_name: Benková
orcid: 0000-0002-8510-9739
- first_name: Alena
full_name: Reková, Alena
last_name: Reková
- first_name: Jaroslava
full_name: Dubová, Jaroslava
last_name: Dubová
- first_name: Jiří
full_name: Malbeck, Jiří
last_name: Malbeck
- first_name: Klaus
full_name: Palme, Klaus
last_name: Palme
- first_name: Břetislav
full_name: Brzobohatý, Břetislav
last_name: Brzobohatý
citation:
ama: Kiran N, Benková E, Reková A, et al. Retargeting a maize β-glucosidase to the
vacuole - Evidence from intact plants that zeatin-O-glucoside is stored in the
vacuole. Phytochemistry. 2012;79:67-77. doi:10.1016/j.phytochem.2012.03.012
apa: Kiran, N., Benková, E., Reková, A., Dubová, J., Malbeck, J., Palme, K., &
Brzobohatý, B. (2012). Retargeting a maize β-glucosidase to the vacuole - Evidence
from intact plants that zeatin-O-glucoside is stored in the vacuole. Phytochemistry.
Elsevier. https://doi.org/10.1016/j.phytochem.2012.03.012
chicago: Kiran, Nagavalli, Eva Benková, Alena Reková, Jaroslava Dubová, Jiří Malbeck,
Klaus Palme, and Břetislav Brzobohatý. “Retargeting a Maize β-Glucosidase to the
Vacuole - Evidence from Intact Plants That Zeatin-O-Glucoside Is Stored in the
Vacuole.” Phytochemistry. Elsevier, 2012. https://doi.org/10.1016/j.phytochem.2012.03.012.
ieee: N. Kiran et al., “Retargeting a maize β-glucosidase to the vacuole
- Evidence from intact plants that zeatin-O-glucoside is stored in the vacuole,”
Phytochemistry, vol. 79. Elsevier, pp. 67–77, 2012.
ista: Kiran N, Benková E, Reková A, Dubová J, Malbeck J, Palme K, Brzobohatý B.
2012. Retargeting a maize β-glucosidase to the vacuole - Evidence from intact
plants that zeatin-O-glucoside is stored in the vacuole. Phytochemistry. 79, 67–77.
mla: Kiran, Nagavalli, et al. “Retargeting a Maize β-Glucosidase to the Vacuole
- Evidence from Intact Plants That Zeatin-O-Glucoside Is Stored in the Vacuole.”
Phytochemistry, vol. 79, Elsevier, 2012, pp. 67–77, doi:10.1016/j.phytochem.2012.03.012.
short: N. Kiran, E. Benková, A. Reková, J. Dubová, J. Malbeck, K. Palme, B. Brzobohatý,
Phytochemistry 79 (2012) 67–77.
date_created: 2018-12-11T12:00:05Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2021-01-12T07:00:25Z
day: '01'
doi: 10.1016/j.phytochem.2012.03.012
extern: 1
fulldoi: https://doi.org/10.1016/j.phytochem.2012.03.012
intvolume: ' 79'
month: '07'
page: 67 - 77
publication: Phytochemistry
publication_status: published
publisher: Elsevier
publist_id: '3886'
quality_controlled: 0
status: public
title: Retargeting a maize β-glucosidase to the vacuole - Evidence from intact plants
that zeatin-O-glucoside is stored in the vacuole
type: journal_article
volume: 79
year: '2012'
...