---
OA_place: repository
OA_type: green
_id: '19372'
abstract:
- lang: eng
  text: We consider the confined Fröhlich polaron and establish an asymptotic series
    for the low-energy eigenvalues in negative powers of the coupling constant. The
    coefficients of the series are derived through a two-fold perturbation approach,
    involving expansions around the electron Pekar minimizer and the excitations of
    the quantum field.
acknowledgement: M.B. gratefully acknowledges funding from the ERC Advanced Grant
  ERC-AdG CLaQS, grant agreement n. 83478.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Morris
  full_name: Brooks, Morris
  id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
  last_name: Brooks
  orcid: 0000-0002-6249-0928
- first_name: David Johannes
  full_name: Mitrouskas, David Johannes
  id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
  last_name: Mitrouskas
citation:
  ama: Brooks M, Mitrouskas DJ.  Asymptotic series for low-energy excitations of the
    Fröhlich polaron at strong coupling. <i>Probability and Mathematical Physics</i>.
    2025;6(1):281-325. doi:<a href="https://doi.org/10.2140/pmp.2025.6.281">10.2140/pmp.2025.6.281</a>
  apa: Brooks, M., &#38; Mitrouskas, D. J. (2025).  Asymptotic series for low-energy
    excitations of the Fröhlich polaron at strong coupling. <i>Probability and Mathematical
    Physics</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/pmp.2025.6.281">https://doi.org/10.2140/pmp.2025.6.281</a>
  chicago: Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for
    Low-Energy Excitations of the Fröhlich Polaron at Strong Coupling.” <i>Probability
    and Mathematical Physics</i>. Mathematical Sciences Publishers, 2025. <a href="https://doi.org/10.2140/pmp.2025.6.281">https://doi.org/10.2140/pmp.2025.6.281</a>.
  ieee: M. Brooks and D. J. Mitrouskas, “ Asymptotic series for low-energy excitations
    of the Fröhlich polaron at strong coupling,” <i>Probability and Mathematical Physics</i>,
    vol. 6, no. 1. Mathematical Sciences Publishers, pp. 281–325, 2025.
  ista: Brooks M, Mitrouskas DJ. 2025.  Asymptotic series for low-energy excitations
    of the Fröhlich polaron at strong coupling. Probability and Mathematical Physics.
    6(1), 281–325.
  mla: Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for Low-Energy
    Excitations of the Fröhlich Polaron at Strong Coupling.” <i>Probability and Mathematical
    Physics</i>, vol. 6, no. 1, Mathematical Sciences Publishers, 2025, pp. 281–325,
    doi:<a href="https://doi.org/10.2140/pmp.2025.6.281">10.2140/pmp.2025.6.281</a>.
  short: M. Brooks, D.J. Mitrouskas, Probability and Mathematical Physics 6 (2025)
    281–325.
corr_author: '1'
date_created: 2025-03-09T23:01:28Z
date_published: 2025-02-23T00:00:00Z
date_updated: 2025-03-10T07:19:02Z
day: '23'
department:
- _id: RoSe
doi: 10.2140/pmp.2025.6.281
external_id:
  arxiv:
  - '2306.16373'
intvolume: '         6'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2306.16373
month: '02'
oa: 1
oa_version: Preprint
page: 281-325
publication: Probability and Mathematical Physics
publication_identifier:
  eissn:
  - 2690-1005
  issn:
  - 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' Asymptotic series for low-energy excitations of the Fröhlich polaron at strong
  coupling'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2025'
...
---
_id: '17074'
abstract:
- lang: eng
  text: We verify Bogoliubov's approximation for translation invariant Bose gases
    in the mean field regime, i.e. we prove that the ground state energy EN is given
    by EN=NeH+infσ(H)+oN→∞(1), where N is the number of particles, eH is the minimal
    Hartree energy and H is the Bogoliubov Hamiltonian. As an intermediate result
    we show the existence of approximate ground states ΨN, i.e. states satisfying
    ⟨HN⟩ΨN=EN+oN→∞(1), exhibiting complete Bose--Einstein condensation with respect
    to one of the Hartree minimizers.
acknowledgement: "We are grateful to Rupert Frank for helpful discussions at an early
  stage of this project.\r\nFunding from the European Union’s Horizon 2020 research
  and innovation programme\r\nunder the ERC grant agreement No 694227 is acknowledged."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Morris
  full_name: Brooks, Morris
  id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425
  last_name: Brooks
  orcid: 0000-0002-6249-0928
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Brooks M, Seiringer R. Validity of Bogoliubov’s approximation fortranslation-invariant
    Bose gases. <i>Probability and Mathematical Physics</i>. 2023;3(4):939-1000. doi:<a
    href="https://doi.org/10.2140/pmp.2022.3.939">10.2140/pmp.2022.3.939</a>
  apa: Brooks, M., &#38; Seiringer, R. (2023). Validity of Bogoliubov’s approximation
    fortranslation-invariant Bose gases. <i>Probability and Mathematical Physics</i>.
    Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/pmp.2022.3.939">https://doi.org/10.2140/pmp.2022.3.939</a>
  chicago: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation
    Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>.
    Mathematical Sciences Publishers, 2023. <a href="https://doi.org/10.2140/pmp.2022.3.939">https://doi.org/10.2140/pmp.2022.3.939</a>.
  ieee: M. Brooks and R. Seiringer, “Validity of Bogoliubov’s approximation fortranslation-invariant
    Bose gases,” <i>Probability and Mathematical Physics</i>, vol. 3, no. 4. Mathematical
    Sciences Publishers, pp. 939–1000, 2023.
  ista: Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant
    Bose gases. Probability and Mathematical Physics. 3(4), 939–1000.
  mla: Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation
    Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>,
    vol. 3, no. 4, Mathematical Sciences Publishers, 2023, pp. 939–1000, doi:<a href="https://doi.org/10.2140/pmp.2022.3.939">10.2140/pmp.2022.3.939</a>.
  short: M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000.
corr_author: '1'
date_created: 2024-05-29T06:12:54Z
date_published: 2023-02-21T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '21'
department:
- _id: RoSe
doi: 10.2140/pmp.2022.3.939
ec_funded: 1
external_id:
  arxiv:
  - '2111.13864'
intvolume: '         3'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2111.13864
month: '02'
oa: 1
oa_version: Preprint
page: 939-1000
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Probability and Mathematical Physics
publication_identifier:
  eissn:
  - 2690-1005
  issn:
  - 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2023'
...
---
_id: '15013'
abstract:
- lang: eng
  text: We consider random n×n matrices X with independent and centered entries and
    a general variance profile. We show that the spectral radius of X converges with
    very high probability to the square root of the spectral radius of the variance
    matrix of X when n tends to infinity. We also establish the optimal rate of convergence,
    that is a new result even for general i.i.d. matrices beyond the explicitly solvable
    Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular
    law [arXiv:1612.07776] at the spectral edge.
acknowledgement: Partially supported by ERC Starting Grant RandMat No. 715539 and
  the SwissMap grant of Swiss National Science Foundation. Partially supported by
  ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center
  for Mathematics in Bonn.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Johannes
  full_name: Alt, Johannes
  id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
  last_name: Alt
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Torben H
  full_name: Krüger, Torben H
  id: 3020C786-F248-11E8-B48F-1D18A9856A87
  last_name: Krüger
  orcid: 0000-0002-4821-3297
citation:
  ama: Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent
    entries. <i>Probability and Mathematical Physics</i>. 2021;2(2):221-280. doi:<a
    href="https://doi.org/10.2140/pmp.2021.2.221">10.2140/pmp.2021.2.221</a>
  apa: Alt, J., Erdös, L., &#38; Krüger, T. H. (2021). Spectral radius of random matrices
    with independent entries. <i>Probability and Mathematical Physics</i>. Mathematical
    Sciences Publishers. <a href="https://doi.org/10.2140/pmp.2021.2.221">https://doi.org/10.2140/pmp.2021.2.221</a>
  chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random
    Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>.
    Mathematical Sciences Publishers, 2021. <a href="https://doi.org/10.2140/pmp.2021.2.221">https://doi.org/10.2140/pmp.2021.2.221</a>.
  ieee: J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with
    independent entries,” <i>Probability and Mathematical Physics</i>, vol. 2, no.
    2. Mathematical Sciences Publishers, pp. 221–280, 2021.
  ista: Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent
    entries. Probability and Mathematical Physics. 2(2), 221–280.
  mla: Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent
    Entries.” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2, Mathematical
    Sciences Publishers, 2021, pp. 221–80, doi:<a href="https://doi.org/10.2140/pmp.2021.2.221">10.2140/pmp.2021.2.221</a>.
  short: J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021)
    221–280.
corr_author: '1'
date_created: 2024-02-18T23:01:03Z
date_published: 2021-05-21T00:00:00Z
date_updated: 2025-04-15T08:05:02Z
day: '21'
department:
- _id: LaEr
doi: 10.2140/pmp.2021.2.221
ec_funded: 1
external_id:
  arxiv:
  - '1907.13631'
intvolume: '         2'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1907.13631
month: '05'
oa: 1
oa_version: Preprint
page: 221-280
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Probability and Mathematical Physics
publication_identifier:
  eissn:
  - 2690-1005
  issn:
  - 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral radius of random matrices with independent entries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2021'
...