---
_id: '10024'
abstract:
- lang: eng
  text: In this paper, we introduce a random environment for the exclusion process
    in  obtained by assigning a maximal occupancy to each site. This maximal occupancy
    is allowed to randomly vary among sites, and partial exclusion occurs. Under the
    assumption of ergodicity under translation and uniform ellipticity of the environment,
    we derive a quenched hydrodynamic limit in path space by strengthening the mild
    solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose,
    we prove, employing the technology developed for the random conductance model,
    a homogenization result in the form of an arbitrary starting point quenched invariance
    principle for a single particle in the same environment, which is a result of
    independent interest. The self-duality property of the partial exclusion process
    allows us to transfer this homogenization result to the particle system and, then,
    apply the tightness criterion in Redig et al. (2020).
acknowledgement: The authors would like to thank Marek Biskup and Alberto Chiarini
  for useful suggestions and  Cristian  Giardina,  Frank  den  Hollander  and  Shubhamoy  Nandan  for  inspiring  discussions.  S.F.  acknowledges  Simona  Villa  for  her  help  in  creating  the  picture.  Furthermore,
  the  authors  thank  two  anonymous  referees  for  the  careful  reading  of  the  manuscript.  S.F.
  acknowledges  financial  support  from  NWO,  The  Netherlands  via  the  grant  TOP1.17.019.
  F.S.  acknowledges  financial  support  from  NWO  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.
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Simone
  full_name: Floreani, Simone
  last_name: Floreani
- first_name: Frank
  full_name: Redig, Frank
  last_name: Redig
- first_name: Federico
  full_name: Sau, Federico
  id: E1836206-9F16-11E9-8814-AEFDE5697425
  last_name: Sau
citation:
  ama: Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process
    in random environment. <i>Stochastic Processes and their Applications</i>. 2021;142:124-158.
    doi:<a href="https://doi.org/10.1016/j.spa.2021.08.006">10.1016/j.spa.2021.08.006</a>
  apa: Floreani, S., Redig, F., &#38; Sau, F. (2021). Hydrodynamics for the partial
    exclusion process in random environment. <i>Stochastic Processes and Their Applications</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.spa.2021.08.006">https://doi.org/10.1016/j.spa.2021.08.006</a>
  chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the
    Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and
    Their Applications</i>. Elsevier, 2021. <a href="https://doi.org/10.1016/j.spa.2021.08.006">https://doi.org/10.1016/j.spa.2021.08.006</a>.
  ieee: S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion
    process in random environment,” <i>Stochastic Processes and their Applications</i>,
    vol. 142. Elsevier, pp. 124–158, 2021.
  ista: Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion
    process in random environment. Stochastic Processes and their Applications. 142,
    124–158.
  mla: Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in
    Random Environment.” <i>Stochastic Processes and Their Applications</i>, vol.
    142, Elsevier, 2021, pp. 124–58, doi:<a href="https://doi.org/10.1016/j.spa.2021.08.006">10.1016/j.spa.2021.08.006</a>.
  short: S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications
    142 (2021) 124–158.
date_created: 2021-09-19T22:01:25Z
date_published: 2021-08-27T00:00:00Z
date_updated: 2023-08-14T06:52:43Z
day: '27'
ddc:
- '519'
department:
- _id: JaMa
doi: 10.1016/j.spa.2021.08.006
ec_funded: 1
external_id:
  arxiv:
  - '1911.12564'
  isi:
  - '000697748500005'
file:
- access_level: open_access
  checksum: 56768c553d7218ee5714902ffec90ec4
  content_type: application/pdf
  creator: dernst
  date_created: 2022-05-13T07:55:50Z
  date_updated: 2022-05-13T07:55:50Z
  file_id: '11370'
  file_name: 2021_StochasticProcessesAppl_Floreani.pdf
  file_size: 2115791
  relation: main_file
  success: 1
file_date_updated: 2022-05-13T07:55:50Z
has_accepted_license: '1'
intvolume: '       142'
isi: 1
keyword:
- hydrodynamic limit
- random environment
- random conductance model
- arbitrary starting point quenched invariance principle
- duality
- mild solution
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 124-158
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Stochastic Processes and their Applications
publication_identifier:
  issn:
  - 0304-4149
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hydrodynamics for the partial exclusion process in random environment
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 142
year: '2021'
...