  The asymmetric simple exclusion process (ASEP) is a paradigmatic
nonequilibrium many-body system that describes the asymmetric random walk of
particles with exclusion interactions in a lattice. Although the ASEP is
recognized as an exactly solvable model, most of the exact results obtained so
far are limited to one-dimensional systems. Here, we construct the exact steady
states of the ASEP with closed and periodic boundary conditions in arbitrary
dimensions. This is achieved through the concept of transition decomposition,
which enables the treatment of the multi-dimensional ASEP as a composite of the
one-dimensional ASEPs.
