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We show that the symmetric simple exclusion process (SSEP) on an countableset is well defined by the stirring graphical construction as soon as thedynamics of a single particle is. The resulting process is Feller, its Markovgenerator is derived on local functions, duality at the level of the empiricaldensity field holds. We then move to the simple exclusion process (SEP) andshow that the graphical construction leads to a well defined Feller processunder a percolation-type assumption corresponding to subcriticality in apercolation with random inhomogeneous parameters. We derive its Markovgenerator on local functions. We discuss applications of the above results toSSEPs and SEPs in random environments, where the standard assumptions toconstruct the process and investigate its basic properties (by the analyticapproach or by graphical constructions) are typically violated. As detailed in[14], our results for SSEP also allow to extend the quenched hydrodynamic limitin path space obtained in [11] by removing Assumption (SEP) used in there.

Graphical constructions of simple exclusion processes with applications to random environments