---
OA_place: publisher
OA_type: hybrid
_id: '18632'
abstract:
- lang: eng
  text: 'For an arbitrary dimension (Formula presented.), we study: the polyharmonic
    Gaussian field (Formula presented.) on the discrete torus (Formula presented.),
    that is the random field whose law on (Formula presented.) given by (Formula presented.)
    where (Formula presented.) is the Lebesgue measure and (Formula presented.) is
    the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG)
    measure associated with it, that is, the random measure on (Formula presented.)
    (Formula presented.) where (Formula presented.) is a regularity parameter. As
    (Formula presented.), we prove convergence of the fields (Formula presented.)
    to the polyharmonic Gaussian field (Formula presented.) on the continuous torus
    (Formula presented.), as well as convergence of the random measures (Formula presented.)
    to the LQG measure (Formula presented.) on (Formula presented.), for all (Formula
    presented.). '
acknowledgement: "KTS is grateful to Christoph Thiele for valuable discussions and
  helpful references. LDS is grateful to Nathanaël Berestycki for valuable discussions
  on Gaussian Multiplicative Chaoses. The authors are grateful to an anonymous reviewer
  for suggestions which improved the presentation.\r\nThe authors gratefully acknowledge
  funding by the Deutsche Forschungsgemeinschaft through the project ‘Random Riemannian
  Geometry’ within the SPP 2265 ‘Random Geometric Systems.'\r\nLDS gratefully acknowledges
  financial support from the European Research Council (grant agreement No. 716117,
  awarded to J. Maas) and from the Austrian Science Fund (FWF). His research was funded
  by the Austrian Science Fund (FWF) project 10.55776/F65 and project 10.55776/ESP208.\r\nRH,
  EK, and KTS gratefully acknowledge funding by the Hausdorff Center for Mathematics
  (project ID 390685813), and through project B03 within the CRC 1060 (project ID
  211504053). RH and KTS also gratefully acknowledges financial support from the European
  Research Council through the ERC AdG ‘RicciBounds’ (grant agreement 694405).\r\nOpen
  access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
  full_name: Dello Schiavo, Lorenzo
  id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
  last_name: Dello Schiavo
  orcid: 0000-0002-9881-6870
- first_name: Ronan
  full_name: Herry, Ronan
  last_name: Herry
- first_name: Eva
  full_name: Kopfer, Eva
  last_name: Kopfer
- first_name: Karl Theodor
  full_name: Sturm, Karl Theodor
  last_name: Sturm
citation:
  ama: 'Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Polyharmonic fields and Liouville
    quantum gravity measures on tori of arbitrary dimension: From discrete to continuous.
    <i>Mathematische Nachrichten</i>. 2025;298(1):244-281. doi:<a href="https://doi.org/10.1002/mana.202400169">10.1002/mana.202400169</a>'
  apa: 'Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2025). Polyharmonic
    fields and Liouville quantum gravity measures on tori of arbitrary dimension:
    From discrete to continuous. <i>Mathematische Nachrichten</i>. Wiley. <a href="https://doi.org/10.1002/mana.202400169">https://doi.org/10.1002/mana.202400169</a>'
  chicago: 'Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm.
    “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary
    Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>. Wiley,
    2025. <a href="https://doi.org/10.1002/mana.202400169">https://doi.org/10.1002/mana.202400169</a>.'
  ieee: 'L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Polyharmonic fields
    and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete
    to continuous,” <i>Mathematische Nachrichten</i>, vol. 298, no. 1. Wiley, pp.
    244–281, 2025.'
  ista: 'Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2025. Polyharmonic fields and
    Liouville quantum gravity measures on tori of arbitrary dimension: From discrete
    to continuous. Mathematische Nachrichten. 298(1), 244–281.'
  mla: 'Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum
    Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.”
    <i>Mathematische Nachrichten</i>, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:<a
    href="https://doi.org/10.1002/mana.202400169">10.1002/mana.202400169</a>.'
  short: L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten
    298 (2025) 244–281.
date_created: 2024-12-08T23:01:56Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2025-04-14T07:27:49Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1002/mana.202400169
ec_funded: 1
external_id:
  arxiv:
  - '2302.02963'
  isi:
  - '001366948500001'
file:
- access_level: open_access
  checksum: 1dc50d156feb777c86d779fb1c9ac875
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  creator: dernst
  date_created: 2025-01-13T10:34:42Z
  date_updated: 2025-01-13T10:34:42Z
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has_accepted_license: '1'
intvolume: '       298'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 244-281
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
  grant_number: E208
  name: Configuration Spaces over Non-Smooth Spaces
publication: Mathematische Nachrichten
publication_identifier:
  eissn:
  - 1522-2616
  issn:
  - 0025-584X
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary
  dimension: From discrete to continuous'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 298
year: '2025'
...