 Exclusion process

Particles on a countable lattice attempt jumps at the rates $p(x,y)$, and an attempt into an occupied site is suppressed. Thus each site contains at most one particle and the number of particles is conserved when finite. Here ${\eta }^{xy}$ interchanges the occupations at $x$ and $y$. Bounded nearest-neighbour rates give a well-defined Markov process. A symmetric jump kernel gives the symmetric simple exclusion process; an unequal left-right kernel gives the asymmetric simple exclusion process.