---
_id: '8973'
abstract:
- lang: eng
  text: We consider the symmetric simple exclusion process in Zd with quenched bounded
    dynamic random conductances and prove its hydrodynamic limit in path space. The
    main tool is the connection, due to the self-duality of the process, between the
    invariance principle for single particles starting from all points and the macroscopic
    behavior of the density field. While the hydrodynamic limit at fixed macroscopic
    times is obtained via a generalization to the time-inhomogeneous context of the
    strategy introduced in [41], in order to prove tightness for the sequence of empirical
    density fields we develop a new criterion based on the notion of uniform conditional
    stochastic continuity, following [50]. In conclusion, we show that uniform elliptic
    dynamic conductances provide an example of environments in which the so-called
    arbitrary starting point invariance principle may be derived from the invariance
    principle of a single particle starting from the origin. Therefore, our hydrodynamics
    result applies to the examples of quenched environments considered in, e.g., [1],
    [3], [6] in combination with the hypothesis of uniform ellipticity.
acknowledgement: "We warmly thank S.R.S. Varadhan for many enlightening discussions
  at an early stage of this work. We are indebted to Francesca Collet for fruitful
  discussions and constant support all throughout this work. We thank Simone Floreani\r\nand
  Alberto Chiarini for helpful conversations on the final part of this paper as well
  as both referees for their careful reading and for raising relevant issues on some
  weak points contained in a previous version of this manuscript; we believe this
  helped us to improve it.\r\nPart of this work was done during the authors’ stay
  at the Institut Henri Poincaré (UMS 5208 CNRS-Sorbonne Université) – Centre Emile
  Borel during the trimester Stochastic Dynamics Out of Equilibrium. The authors thank
  this institution for hospitality and support (through LabEx CARMIN, ANR-10-LABX-59-01).
  F.S. thanks laboratoire\r\nMAP5 of Université de Paris, and E.S. thanks Delft University,
  for financial support and hospitality. F.S. acknowledges NWO for financial support
  via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon
  2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement
  No. 754411. This research has been conducted within the FP2M federation (CNRS FR
  2036)."
article_number: '138'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Frank
  full_name: Redig, Frank
  last_name: Redig
- first_name: Ellen
  full_name: Saada, Ellen
  last_name: Saada
- first_name: Federico
  full_name: Sau, Federico
  id: E1836206-9F16-11E9-8814-AEFDE5697425
  last_name: Sau
citation:
  ama: 'Redig F, Saada E, Sau F. Symmetric simple exclusion process in dynamic environment:
    Hydrodynamics. <i>Electronic Journal of Probability</i>. 2020;25. doi:<a href="https://doi.org/10.1214/20-EJP536">10.1214/20-EJP536</a>'
  apa: 'Redig, F., Saada, E., &#38; Sau, F. (2020). Symmetric simple exclusion process
    in dynamic environment: Hydrodynamics. <i>Electronic Journal of Probability</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/20-EJP536">https://doi.org/10.1214/20-EJP536</a>'
  chicago: 'Redig, Frank, Ellen Saada, and Federico Sau. “Symmetric Simple Exclusion
    Process in Dynamic Environment: Hydrodynamics.” <i>Electronic Journal of Probability</i>.
    Institute of Mathematical Statistics, 2020. <a href="https://doi.org/10.1214/20-EJP536">https://doi.org/10.1214/20-EJP536</a>.'
  ieee: 'F. Redig, E. Saada, and F. Sau, “Symmetric simple exclusion process in dynamic
    environment: Hydrodynamics,” <i>Electronic Journal of Probability</i>, vol. 25.
    Institute of Mathematical Statistics, 2020.'
  ista: 'Redig F, Saada E, Sau F. 2020. Symmetric simple exclusion process in dynamic
    environment: Hydrodynamics. Electronic Journal of Probability. 25, 138.'
  mla: 'Redig, Frank, et al. “Symmetric Simple Exclusion Process in Dynamic Environment:
    Hydrodynamics.” <i>Electronic Journal of Probability</i>, vol. 25, 138, Institute
    of Mathematical Statistics, 2020, doi:<a href="https://doi.org/10.1214/20-EJP536">10.1214/20-EJP536</a>.'
  short: F. Redig, E. Saada, F. Sau, Electronic Journal of Probability 25 (2020).
das_tickbox: '1'
date_created: 2020-12-27T23:01:17Z
date_published: 2020-10-21T00:00:00Z
date_updated: 2026-07-06T12:04:40Z
day: '21'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/20-EJP536
ec_funded: 1
external_id:
  arxiv:
  - '1811.01366'
  isi:
  - '000591737500001'
file:
- access_level: open_access
  checksum: d75359b9814e78d57c0a481b7cde3751
  content_type: application/pdf
  creator: dernst
  date_created: 2020-12-28T08:24:08Z
  date_updated: 2020-12-28T08:24:08Z
  file_id: '8976'
  file_name: 2020_ElectronJProbab_Redig.pdf
  file_size: 696653
  relation: main_file
  success: 1
file_date_updated: 2020-12-28T08:24:08Z
fulldoi: https://doi.org/10.1214/20-EJP536
has_accepted_license: '1'
intvolume: '        25'
isi: 1
language:
- iso: eng
month: '10'
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: 'Symmetric simple exclusion process in dynamic environment: Hydrodynamics'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2020'
...