---
_id: '11732'
abstract:
- lang: eng
text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic
formula, which strongly depends on the strength of the interaction potential V
on the Fermi surface. In combination with the recent result by one of us (Math.
Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities,
we prove the universality of the ratio of the energy gap and the critical temperature.
acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and
many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges
partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open
access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of
Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9
apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9
chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap
at High Density.” Journal of Statistical Physics. Springer Nature, 2022.
https://doi.org/10.1007/s10955-022-02965-9.
ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal
of Statistical Physics, vol. 189. Springer Nature, 2022.
ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal
of Statistical Physics. 189, 5.
mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at
High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature,
2022, doi:10.1007/s10955-022-02965-9.
short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).
date_created: 2022-08-05T11:36:56Z
date_published: 2022-07-29T00:00:00Z
date_updated: 2023-09-05T14:57:49Z
day: '29'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1007/s10955-022-02965-9
ec_funded: 1
external_id:
isi:
- '000833007200002'
file:
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checksum: b398c4dbf65f71d417981d6e366427e9
content_type: application/pdf
creator: dernst
date_created: 2022-08-08T07:36:34Z
date_updated: 2022-08-08T07:36:34Z
file_id: '11746'
file_name: 2022_JourStatisticalPhysics_Henheik.pdf
file_size: 419563
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file_date_updated: 2022-08-08T07:36:34Z
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intvolume: ' 189'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The BCS energy gap at high density
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: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 189
year: '2022'
...
---
_id: '10285'
abstract:
- lang: eng
text: We study the overlaps between right and left eigenvectors for random matrices
of the spherical ensemble, as well as truncated unitary ensembles in the regime
where half of the matrix at least is truncated. These two integrable models exhibit
a form of duality, and the essential steps of our investigation can therefore
be performed in parallel. In every case, conditionally on all eigenvalues, diagonal
overlaps are shown to be distributed as a product of independent random variables
with explicit distributions. This enables us to prove that the scaled diagonal
overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail
limit, namely, the inverse of a γ2 distribution. We also provide formulae for
the conditional expectation of diagonal and off-diagonal overlaps, either with
respect to one eigenvalue, or with respect to the whole spectrum. These results,
analogous to what is known for the complex Ginibre ensemble, can be obtained in
these cases thanks to integration techniques inspired from a previous work by
Forrester & Krishnapur.
acknowledgement: We acknowledge partial support from the grants NSF DMS-1812114 of
P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has
also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would
like to thank Paul Bourgade and László Erdős for many helpful comments.
article_number: '124'
article_processing_charge: No
article_type: original
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
citation:
ama: Dubach G. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686
apa: Dubach, G. (2021). On eigenvector statistics in the spherical and truncated
unitary ensembles. Electronic Journal of Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/21-EJP686
chicago: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2021. https://doi.org/10.1214/21-EJP686.
ieee: G. Dubach, “On eigenvector statistics in the spherical and truncated unitary
ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical
Statistics, 2021.
ista: Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 26, 124.
mla: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute
of Mathematical Statistics, 2021, doi:10.1214/21-EJP686.
short: G. Dubach, Electronic Journal of Probability 26 (2021).
date_created: 2021-11-14T23:01:25Z
date_published: 2021-09-28T00:00:00Z
date_updated: 2021-11-15T10:48:46Z
day: '28'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1214/21-EJP686
ec_funded: 1
file:
- access_level: open_access
checksum: 1c975afb31460277ce4d22b93538e5f9
content_type: application/pdf
creator: cchlebak
date_created: 2021-11-15T10:10:17Z
date_updated: 2021-11-15T10:10:17Z
file_id: '10288'
file_name: 2021_ElecJournalProb_Dubach.pdf
file_size: 735940
relation: main_file
success: 1
file_date_updated: 2021-11-15T10:10:17Z
has_accepted_license: '1'
intvolume: ' 26'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On eigenvector statistics in the spherical and truncated unitary ensembles
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: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 26
year: '2021'
...
---
_id: '9230'
abstract:
- lang: eng
text: "We consider a model of the Riemann zeta function on the critical axis and
study its maximum over intervals of length (log T)θ, where θ is either fixed or
tends to zero at a suitable rate.\r\nIt is shown that the deterministic level
of the maximum interpolates smoothly between the ones\r\nof log-correlated variables
and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to
1/4’ in the second order. This provides a natural context where extreme value
statistics of\r\nlog-correlated variables with time-dependent variance and rate
occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate
for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian
correction. This correction is expected to be present for the\r\nRiemann zeta
function and pertains to the question of the correct order of the maximum of\r\nthe
zeta function in large intervals."
acknowledgement: The research of L.-P. A. is supported in part by the grant NSF CAREER
DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID
443891315 within SPP 2265 and Project-ID 446173099.
article_number: '2103.04817'
article_processing_charge: No
author:
- first_name: Louis-Pierre
full_name: Arguin, Louis-Pierre
last_name: Arguin
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: Lisa
full_name: Hartung, Lisa
last_name: Hartung
citation:
ama: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817
apa: Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model
of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817
chicago: Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a
Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2103.04817.
ieee: L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the
Riemann zeta function over intervals of varying length,” arXiv. .
ista: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv, 2103.04817.
mla: Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta
Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.
short: L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).
date_created: 2021-03-09T11:08:15Z
date_published: 2021-03-08T00:00:00Z
date_updated: 2023-05-03T10:22:59Z
day: '08'
department:
- _id: LaEr
doi: 10.48550/arXiv.2103.04817
ec_funded: 1
external_id:
arxiv:
- '2103.04817'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.04817
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
status: public
title: Maxima of a random model of the Riemann zeta function over intervals of varying
length
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9281'
abstract:
- lang: eng
text: We comment on two formal proofs of Fermat's sum of two squares theorem, written
using the Mathematical Components libraries of the Coq proof assistant. The first
one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's
recent new proof relying on partition-theoretic arguments. Both formal proofs
rely on a general property of involutions of finite sets, of independent interest.
The proof technique consists for the most part of automating recurrent tasks (such
as case distinctions and computations on natural numbers) via ad hoc tactics.
article_number: '2103.11389'
article_processing_charge: No
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: Fabian
full_name: Mühlböck, Fabian
id: 6395C5F6-89DF-11E9-9C97-6BDFE5697425
last_name: Mühlböck
orcid: 0000-0003-1548-0177
citation:
ama: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv.
doi:10.48550/arXiv.2103.11389
apa: Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence
proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389
chicago: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s
One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389.
ieee: G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,”
arXiv. .
ista: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof.
arXiv, 2103.11389.
mla: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence
Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389.
short: G. Dubach, F. Mühlböck, ArXiv (n.d.).
date_created: 2021-03-23T05:38:48Z
date_published: 2021-03-21T00:00:00Z
date_updated: 2023-05-03T10:26:45Z
day: '21'
department:
- _id: LaEr
- _id: ToHe
doi: 10.48550/arXiv.2103.11389
ec_funded: 1
external_id:
arxiv:
- '2103.11389'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.11389
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '9946'
relation: other
status: public
status: public
title: Formal verification of Zagier's one-sentence proof
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '8373'
abstract:
- lang: eng
text: It is well known that special Kubo-Ando operator means admit divergence center
interpretations, moreover, they are also mean squared error estimators for certain
metrics on positive definite operators. In this paper we give a divergence center
interpretation for every symmetric Kubo-Ando mean. This characterization of the
symmetric means naturally leads to a definition of weighted and multivariate versions
of a large class of symmetric Kubo-Ando means. We study elementary properties
of these weighted multivariate means, and note in particular that in the special
case of the geometric mean we recover the weighted A#H-mean introduced by Kim,
Lawson, and Lim.
acknowledgement: "The authors are grateful to Milán Mosonyi for fruitful discussions
on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ.
Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant
for Quantum Information Theory, No. 96 141, and by Hungarian National Research,
Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and
no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute
of Science and Technology Austria (project code IC1027FELL01), by the European Union's
Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant
Agreement No. 846294, and partially supported by the Hungarian National Research,
Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601."
article_processing_charge: No
article_type: original
author:
- first_name: József
full_name: Pitrik, József
last_name: Pitrik
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Pitrik J, Virosztek D. A divergence center interpretation of general symmetric
Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra
and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007
apa: Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation
of general symmetric Kubo-Ando means, and related weighted multivariate operator
means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007
chicago: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation
of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator
Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007.
ieee: J. Pitrik and D. Virosztek, “A divergence center interpretation of general
symmetric Kubo-Ando means, and related weighted multivariate operator means,”
Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021.
ista: Pitrik J, Virosztek D. 2021. A divergence center interpretation of general
symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear
Algebra and its Applications. 609, 203–217.
mla: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of
General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator
Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021,
pp. 203–17, doi:10.1016/j.laa.2020.09.007.
short: J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.
date_created: 2020-09-11T08:35:50Z
date_published: 2021-01-15T00:00:00Z
date_updated: 2023-08-04T10:58:14Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.laa.2020.09.007
ec_funded: 1
external_id:
arxiv:
- '2002.11678'
isi:
- '000581730500011'
intvolume: ' 609'
isi: 1
keyword:
- Kubo-Ando mean
- weighted multivariate mean
- barycenter
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.11678
month: '01'
oa: 1
oa_version: Preprint
page: 203-217
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Linear Algebra and its Applications
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: A divergence center interpretation of general symmetric Kubo-Ando means, and
related weighted multivariate operator means
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 609
year: '2021'
...