---
_id: '10613'
abstract:
- lang: eng
  text: Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci,
    and Redig, we first provide a general framework for the study of scaling limits
    of higher-order fields. Then, by considering the same class of infinite interacting
    particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion
    and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic
    limit, and convergence for the equilibrium fluctuations, of higher-order fields.
    In particular, the limit fields exhibit a tensor structure. Our fluctuation result
    differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional
    Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium
    fluctuations, of higher-order fields. In particular, the limit fields exhibit
    a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}],
    since we consider a different notion of higher-order fluctuation fields.
acknowledgement: "F.S. would like to thank Mario Ayala and Frank Redig for useful
  discussions. J.P.C. acknowledges partial financial support from the US National
  Science Foundation (DMS-1855604). F.S. was financially supported by the European
  Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie
  grant agreement No. 754411.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Joe P.
  full_name: Chen, Joe P.
  last_name: Chen
- first_name: Federico
  full_name: Sau, Federico
  id: E1836206-9F16-11E9-8814-AEFDE5697425
  last_name: Sau
citation:
  ama: Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of
    interacting particle systems. <i>Markov Processes And Related Fields</i>. 2021;27(3):339-380.
  apa: Chen, J. P., &#38; Sau, F. (2021). Higher-order hydrodynamics and equilibrium
    fluctuations of interacting particle systems. <i>Markov Processes And Related
    Fields</i>. Polymat Publishing.
  chicago: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
    Fluctuations of Interacting Particle Systems.” <i>Markov Processes And Related
    Fields</i>. Polymat Publishing, 2021.
  ieee: J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations
    of interacting particle systems,” <i>Markov Processes And Related Fields</i>,
    vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.
  ista: Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations
    of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.
  mla: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
    Fluctuations of Interacting Particle Systems.” <i>Markov Processes And Related
    Fields</i>, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80.
  short: J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.
date_created: 2022-01-10T14:02:31Z
date_published: 2021-03-16T00:00:00Z
date_updated: 2022-01-10T15:29:08Z
day: '16'
department:
- _id: JaMa
ec_funded: 1
external_id:
  arxiv:
  - '2008.13403'
intvolume: '        27'
issue: '3'
keyword:
- interacting particle systems
- higher-order fields
- hydrodynamic limit
- equilibrium fluctuations
- duality
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2008.13403
month: '03'
oa: 1
oa_version: Preprint
page: 339-380
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Markov Processes And Related Fields
publication_identifier:
  issn:
  - 1024-2953
publication_status: published
publisher: Polymat Publishing
quality_controlled: '1'
related_material:
  link:
  - description: Link to Abstract on publisher's website
    relation: other
    url: http://math-mprf.org/journal/articles/id1614/
  - description: Referred to in Abstract
    relation: used_for_analysis_in
    url: https://arxiv.org/abs/2004.08412
status: public
title: Higher-order hydrodynamics and equilibrium fluctuations of interacting particle
  systems
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 27
year: '2021'
...