 Symmetric simple exclusion process

On $\mathbb{Z}$, put independent rate-$c$ Poisson processes on unoriented nearest-neighbour edges, and exchange their endpoint occupations at each mark. Its generator on cylinder functions is $Lf(\eta )=c{\sum }_x[f({\eta }^{x,x+1})-f(\eta )]$. Equal occupations do not change the state, and a particle next to a vacancy jumps across at rate $c$. The stirring representation of symmetric exclusion constructs it for arbitrary initial configurations. The simple occupation-product product self-duality of symmetric exclusion requires symmetry and is not the ordinary duality of an asymmetric process.