TY - JOUR AB - 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. AU - Franceschini, Chiara AU - Gonçalves, Patrícia AU - Sau, Federico ID - 12281 IS - 2 JF - Bernoulli KW - Statistics and Probability SN - 1350-7265 TI - Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics VL - 28 ER - TY - JOUR AB - 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. AU - Floreani, Simone AU - Redig, Frank AU - Sau, Federico ID - 10797 IS - 1 JF - Annales de l'institut Henri Poincare (B) Probability and Statistics SN - 0246-0203 TI - Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations VL - 58 ER - TY - JOUR AB - 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. AU - Chen, Joe P. AU - Sau, Federico ID - 10613 IS - 3 JF - Markov Processes And Related Fields KW - interacting particle systems KW - higher-order fields KW - hydrodynamic limit KW - equilibrium fluctuations KW - duality SN - 1024-2953 TI - Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems VL - 27 ER - TY - JOUR AB - 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). AU - Floreani, Simone AU - Redig, Frank AU - Sau, Federico ID - 10024 JF - Stochastic Processes and their Applications KW - hydrodynamic limit KW - random environment KW - random conductance model KW - arbitrary starting point quenched invariance principle KW - duality KW - mild solution SN - 0304-4149 TI - Hydrodynamics for the partial exclusion process in random environment VL - 142 ER - TY - JOUR AB - 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. AU - Redig, Frank AU - Saada, Ellen AU - Sau, Federico ID - 8973 JF - Electronic Journal of Probability TI - Symmetric simple exclusion process in dynamic environment: Hydrodynamics VL - 25 ER -