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In order to illuminate the properties of current fluctuations in more thanone dimension, we use a lattice-based Markov process driven into anon-equilibrium steady state. Specifically, we perform a detailed study of theparticle current fluctuations in a two-dimensional zero-range process with openboundary conditions and probe the influence of the underlying geometry bycomparing results from a square and a triangular lattice. Moreover, we examinethe structure of local currents corresponding to a given global currentfluctuation and comment on the role of spatial inhomogeneities for thediscrepancies observed in testing some recent fluctuation symmetries.

Local structure of current fluctuations in diffusive systems beyond one dimension