= Exclusion process
{title2=$Lf(\eta)=\sum_{x,y}p(x,y)\eta(x)(1-\eta(y))[f(\eta^{xy})-f(\eta)]$}
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>.
Back to article page
