---
_id: '7900'
abstract:
- lang: eng
text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic
systems. However, it suffers from some defects in predicting physical properties,
making necessary a theory of quantum correlations. Recently, bosonization of many-body
correlations has been rigorously justified as an upper bound on the correlation
energy at high density with weak interactions. We review the bosonic approximation,
deriving an effective Hamiltonian. We then show that for systems with Coulomb
interaction this effective theory predicts collective excitations (plasmons) in
accordance with the random phase approximation of Bohm and Pines, and with experimental
observation.
article_number: '2060009'
article_processing_charge: No
article_type: original
author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
citation:
ama: Benedikter NP. Bosonic collective excitations in Fermi gases. Reviews in
Mathematical Physics. 2021;33(1). doi:10.1142/s0129055x20600090
apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. Reviews
in Mathematical Physics. World Scientific. https://doi.org/10.1142/s0129055x20600090
chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews
in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/s0129055x20600090.
ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” Reviews
in Mathematical Physics, vol. 33, no. 1. World Scientific, 2021.
ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews
in Mathematical Physics. 33(1), 2060009.
mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews
in Mathematical Physics, vol. 33, no. 1, 2060009, World Scientific, 2021,
doi:10.1142/s0129055x20600090.
short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-05-28T16:47:55Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-09-05T16:07:40Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600090
ec_funded: 1
external_id:
arxiv:
- '1910.08190'
isi:
- '000613313200010'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.08190
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonic collective excitations in Fermi gases
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '10852'
abstract:
- lang: eng
text: ' We review old and new results on the Fröhlich polaron model. The discussion
includes the validity of the (classical) Pekar approximation in the strong coupling
limit, quantum corrections to this limit, as well as the divergence of the effective
polaron mass.'
acknowledgement: This work was supported by the European Research Council (ERC) under
the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo.
694227).
article_number: '2060012'
article_processing_charge: No
article_type: original
author:
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Seiringer R. The polaron at strong coupling. Reviews in Mathematical Physics.
2021;33(01). doi:10.1142/s0129055x20600120
apa: Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical
Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120
chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120.
ieee: R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical
Physics, vol. 33, no. 01. World Scientific Publishing, 2021.
ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical
Physics. 33(01), 2060012.
mla: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical
Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120.
short: R. Seiringer, Reviews in Mathematical Physics 33 (2021).
date_created: 2022-03-18T08:11:34Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-05T16:08:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600120
ec_funded: 1
external_id:
arxiv:
- '1912.12509'
isi:
- '000613313200013'
intvolume: ' 33'
isi: 1
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.12509
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The polaron at strong coupling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '9056'
abstract:
- lang: eng
text: "In this thesis we study persistence of multi-covers of Euclidean balls and
the geometric structures underlying their computation, in particular Delaunay
mosaics and Voronoi tessellations. The k-fold cover for some discrete input point
set consists of the space where at least k balls of radius r around the input
points overlap. Persistence is a notion that captures, in some sense, the topology
of the shape underlying the input. While persistence is usually computed for the
union of balls, the k-fold cover is of interest as it captures local density,\r\nand
thus might approximate the shape of the input better if the input data is noisy.
To compute persistence of these k-fold covers, we need a discretization that is
provided by higher-order Delaunay mosaics. We present and implement a simple and
efficient algorithm for the computation of higher-order Delaunay mosaics, and
use it to give experimental results for their combinatorial properties. The algorithm
makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order
Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the
tiling, we also obtain higher-order α-shapes as slices. These allow us to compute
persistence of the multi-covers for varying radius r; the computation for varying
k is less straight-foward and involves the rhomboid tiling directly. We apply
our algorithms to experimental sphere packings to shed light on their structural
properties. Finally, inspired by periodic structures in packings and materials,
we propose and implement an algorithm for periodic Delaunay triangulations to
be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss
the implications on persistence for periodic data sets."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056
apa: Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute
of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056
chicago: Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute
of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.
ieee: G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of
Science and Technology Austria, Klosterneuburg, 2021.
ista: 'Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg:
Institute of Science and Technology Austria.'
mla: Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute
of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.
short: G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science
and Technology Austria, 2021.
date_created: 2021-02-02T14:11:06Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-07T13:29:01Z
day: '01'
ddc:
- '006'
- '514'
- '516'
degree_awarded: PhD
department:
- _id: HeEd
- _id: GradSch
doi: 10.15479/AT:ISTA:9056
file:
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checksum: bcf27986147cab0533b6abadd74e7629
content_type: application/zip
creator: patrickd
date_created: 2021-02-02T14:09:25Z
date_updated: 2021-02-03T10:37:28Z
file_id: '9063'
file_name: thesis_source.zip
file_size: 13446994
relation: source_file
- access_level: open_access
checksum: 9cc8af266579a464385bbe2aff6af606
content_type: application/pdf
creator: patrickd
date_created: 2021-02-02T14:09:18Z
date_updated: 2021-02-02T14:09:18Z
file_id: '9064'
file_name: thesis_pdfA2b.pdf
file_size: 5210329
relation: main_file
success: 1
file_date_updated: 2021-02-03T10:37:28Z
has_accepted_license: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '134'
place: Klosterneuburg
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '187'
relation: part_of_dissertation
status: public
- id: '8703'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
title: Multi-cover persistence and Delaunay mosaics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '9022'
abstract:
- lang: eng
text: "In the first part of the thesis we consider Hermitian random matrices. Firstly,
we consider sample covariance matrices XX∗ with X having independent identically
distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences
of linear statistics of XX∗ and its minor after removing the first column of X.
Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics
near cusp singularities of the limiting density of states are universal and that
they form a Pearcey process. Since the limiting eigenvalue distribution admits
only square root (edge) and cubic root (cusp) singularities, this concludes the
third and last remaining case of the Wigner-Dyson-Mehta universality conjecture.
The main technical ingredients are an optimal local law at the cusp, and the proof
of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp
regime.\r\nIn the second part we consider non-Hermitian matrices X with centred
i.i.d. entries. We normalise the entries of X to have variance N −1. It is well
known that the empirical eigenvalue density converges to the uniform distribution
on the unit disk (circular law). In the first project, we prove universality of
the local eigenvalue statistics close to the edge of the spectrum. This is the
non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically
we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck
flow for very long time\r\n(up to t = +∞). In the second project, we consider
linear statistics of eigenvalues for macroscopic test functions f in the Sobolev
space H2+ϵ and prove their convergence to the projection of the Gaussian Free
Field on the unit disk. We prove this result for non-Hermitian matrices with real
or complex entries. The main technical ingredients are: (i) local law for products
of two resolvents at different spectral parameters, (ii) analysis of correlated
Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically
rigorous application of supersymmetric techniques (SUSY ) to give a lower tail
estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we
use superbosonisation formula to give an integral representation of the resolvent
of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex
and real case, respectively. The rigorous analysis of these integrals is quite
challenging since simple saddle point analysis cannot be applied (the main contribution
comes from a non-trivial manifold). Our result\r\nimproves classical smoothing
inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality
for i.i.d. non-Hermitian matrices."
acknowledgement: I gratefully acknowledge the financial support from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
citation:
ama: Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022
apa: Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022
chicago: Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.”
Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.
ieee: G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute
of Science and Technology Austria, 2021.
ista: Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute
of Science and Technology Austria.
mla: Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices.
Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022.
short: G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute
of Science and Technology Austria, 2021.
date_created: 2021-01-21T18:16:54Z
date_published: 2021-01-25T00:00:00Z
date_updated: 2023-09-07T13:29:32Z
day: '25'
ddc:
- '510'
degree_awarded: PhD
department:
- _id: GradSch
- _id: LaEr
doi: 10.15479/AT:ISTA:9022
ec_funded: 1
file:
- access_level: open_access
checksum: 5a93658a5f19478372523ee232887e2b
content_type: application/pdf
creator: gcipollo
date_created: 2021-01-25T14:19:03Z
date_updated: 2021-01-25T14:19:03Z
file_id: '9043'
file_name: thesis.pdf
file_size: 4127796
relation: main_file
success: 1
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checksum: e8270eddfe6a988e92a53c88d1d19b8c
content_type: application/zip
creator: gcipollo
date_created: 2021-01-25T14:19:10Z
date_updated: 2021-01-25T14:19:10Z
file_id: '9044'
file_name: Thesis_files.zip
file_size: 12775206
relation: source_file
file_date_updated: 2021-01-25T14:19:10Z
has_accepted_license: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: '380'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: Fluctuations in the spectrum of random matrices
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '9416'
abstract:
- lang: eng
text: 'We study the inductive bias of two-layer ReLU networks trained by gradient
flow. We identify a class of easy-to-learn (`orthogonally separable'') datasets,
and characterise the solution that ReLU networks trained on such datasets converge
to. Irrespective of network width, the solution turns out to be a combination
of two max-margin classifiers: one corresponding to the positive data subset and
one corresponding to the negative data subset. The proof is based on the recently
introduced concept of extremal sectors, for which we prove a number of properties
in the context of orthogonal separability. In particular, we prove stationarity
of activation patterns from some time onwards, which enables a reduction of the
ReLU network to an ensemble of linear subnetworks.'
article_processing_charge: No
author:
- first_name: Phuong
full_name: Bui Thi Mai, Phuong
id: 3EC6EE64-F248-11E8-B48F-1D18A9856A87
last_name: Bui Thi Mai
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Phuong M, Lampert C. The inductive bias of ReLU networks on orthogonally separable
data. In: 9th International Conference on Learning Representations. ; 2021.'
apa: Phuong, M., & Lampert, C. (2021). The inductive bias of ReLU networks on
orthogonally separable data. In 9th International Conference on Learning Representations.
Virtual.
chicago: Phuong, Mary, and Christoph Lampert. “The Inductive Bias of ReLU Networks
on Orthogonally Separable Data.” In 9th International Conference on Learning
Representations, 2021.
ieee: M. Phuong and C. Lampert, “The inductive bias of ReLU networks on orthogonally
separable data,” in 9th International Conference on Learning Representations,
Virtual, 2021.
ista: 'Phuong M, Lampert C. 2021. The inductive bias of ReLU networks on orthogonally
separable data. 9th International Conference on Learning Representations. ICLR:
International Conference on Learning Representations.'
mla: Phuong, Mary, and Christoph Lampert. “The Inductive Bias of ReLU Networks on
Orthogonally Separable Data.” 9th International Conference on Learning Representations,
2021.
short: M. Phuong, C. Lampert, in:, 9th International Conference on Learning Representations,
2021.
conference:
end_date: 2021-05-07
location: Virtual
name: ' ICLR: International Conference on Learning Representations'
start_date: 2021-05-03
date_created: 2021-05-24T11:16:46Z
date_published: 2021-05-01T00:00:00Z
date_updated: 2023-09-07T13:29:50Z
day: '01'
ddc:
- '000'
department:
- _id: GradSch
- _id: ChLa
file:
- access_level: open_access
checksum: f34ff17017527db5ba6927f817bdd125
content_type: application/pdf
creator: bphuong
date_created: 2021-05-24T11:15:57Z
date_updated: 2021-05-24T11:15:57Z
file_id: '9417'
file_name: iclr2021_conference.pdf
file_size: 502356
relation: main_file
file_date_updated: 2021-05-24T11:15:57Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://openreview.net/pdf?id=krz7T0xU9Z_
month: '05'
oa: 1
oa_version: Published Version
publication: 9th International Conference on Learning Representations
publication_status: published
quality_controlled: '1'
related_material:
record:
- id: '9418'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: The inductive bias of ReLU networks on orthogonally separable data
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...