--- _id: '12281' abstract: - lang: eng text: We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle. acknowledgement: "C.F. and P.G. thank FCT/Portugal for support through the project UID/MAT/04459/2013.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No. 715734). F.S. was founded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\nF.S. wishes to thank Joe P. Chen for some fruitful discussions at an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this work has been done, and the European research and innovative programme No. 715734 for the kind hospitality." article_processing_charge: No article_type: original author: - first_name: Chiara full_name: Franceschini, Chiara last_name: Franceschini - first_name: Patrícia full_name: Gonçalves, Patrícia last_name: Gonçalves - first_name: Federico full_name: Sau, Federico id: E1836206-9F16-11E9-8814-AEFDE5697425 last_name: Sau citation: ama: 'Franceschini C, Gonçalves P, Sau F. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 2022;28(2):1340-1381. doi:10.3150/21-bej1390' apa: 'Franceschini, C., Gonçalves, P., & Sau, F. (2022). Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/21-bej1390' chicago: 'Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2022. https://doi.org/10.3150/21-bej1390.' ieee: 'C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics,” Bernoulli, vol. 28, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381, 2022.' ista: 'Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.' mla: 'Franceschini, Chiara, et al. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” Bernoulli, vol. 28, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2022, pp. 1340–81, doi:10.3150/21-bej1390.' short: C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381. date_created: 2023-01-16T10:03:04Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-04T10:27:35Z day: '01' department: - _id: JaMa doi: 10.3150/21-bej1390 ec_funded: 1 external_id: arxiv: - '2007.11998' isi: - '000766619100025' intvolume: ' 28' isi: 1 issue: '2' keyword: - Statistics and Probability language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2007.11998 month: '05' oa: 1 oa_version: Preprint page: 1340-1381 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Bernoulli publication_identifier: issn: - 1350-7265 publication_status: published publisher: Bernoulli Society for Mathematical Statistics and Probability quality_controlled: '1' scopus_import: '1' status: public title: 'Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 28 year: '2022' ... --- _id: '10797' abstract: - lang: eng text: We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n-point correlation functions in the non-equilibrium steady state for systems with at most two different reservoir parameters, such as a chain with reservoirs at left and right ends. - lang: fre text: Nous considérons des processus d’exclusion partielle, et des processus d’inclusion sur un graphe général en contact avec des réservoirs. Nous autorisons la présence de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir des dualités orthogonales nous démontrons des propriétés universelles des fonctions de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec des réservoirs à droite et à gauche. acknowledgement: The authors would like to thank Gioia Carinci and Cristian Giardinà for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT (Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay University), where part of this work was performed. S.F. acknowledges Simona Villa for her support in creating the picture. S.F. acknowledges financial support from NWO via the grant TOP1.17.019. F.S. acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411. article_processing_charge: No article_type: original 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. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2022;58(1):220-247. doi:10.1214/21-AIHP1163 apa: Floreani, S., Redig, F., & Sau, F. (2022). Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AIHP1163 chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AIHP1163. ieee: S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1. Institute of Mathematical Statistics, pp. 220–247, 2022. ista: Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 58(1), 220–247. mla: Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 1, Institute of Mathematical Statistics, 2022, pp. 220–47, doi:10.1214/21-AIHP1163. short: S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability and Statistics 58 (2022) 220–247. date_created: 2022-02-27T23:01:50Z date_published: 2022-02-01T00:00:00Z date_updated: 2023-10-17T12:49:43Z day: '01' department: - _id: JaMa doi: 10.1214/21-AIHP1163 ec_funded: 1 external_id: arxiv: - '2007.08272' isi: - '000752489300010' intvolume: ' 58' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2007.08272 month: '02' oa: 1 oa_version: Preprint page: 220-247 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Annales de l'institut Henri Poincare (B) Probability and Statistics publication_identifier: issn: - 0246-0203 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 58 year: '2022' ... --- _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 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' ... --- _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 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 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: '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 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. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP536' apa: 'Redig, F., Saada, E., & Sau, F. (2020). Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP536' chicago: 'Redig, Frank, Ellen Saada, and Federico Sau. “Symmetric Simple Exclusion Process in Dynamic Environment: Hydrodynamics.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP536.' ieee: 'F. Redig, E. Saada, and F. Sau, “Symmetric simple exclusion process in dynamic environment: Hydrodynamics,” Electronic Journal of Probability, 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.” Electronic Journal of Probability, vol. 25, 138, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP536.' short: F. Redig, E. Saada, F. Sau, Electronic Journal of Probability 25 (2020). date_created: 2020-12-27T23:01:17Z date_published: 2020-10-21T00:00:00Z date_updated: 2023-10-17T12:51:56Z 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 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' ...