---
_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. Stochastic Processes and their Applications. 2021;142:124-158.
doi:10.1016/j.spa.2021.08.006
apa: Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial
exclusion process in random environment. Stochastic Processes and Their Applications.
Elsevier. https://doi.org/10.1016/j.spa.2021.08.006
chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the
Partial Exclusion Process in Random Environment.” Stochastic Processes and
Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.
ieee: S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion
process in random environment,” Stochastic Processes and their Applications,
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.” Stochastic Processes and Their Applications, vol.
142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006.
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
license: https://creativecommons.org/licenses/by/4.0/
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'
...
---
_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. Markov Processes And Related Fields. 2021;27(3):339-380.
apa: Chen, J. P., & Sau, F. (2021). Higher-order hydrodynamics and equilibrium
fluctuations of interacting particle systems. Markov Processes And Related
Fields. Polymat Publishing.
chicago: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
Fluctuations of Interacting Particle Systems.” Markov Processes And Related
Fields. Polymat Publishing, 2021.
ieee: J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations
of interacting particle systems,” Markov Processes And Related Fields,
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.” Markov Processes And Related
Fields, 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'
...