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 - 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 - 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 -