= Bernoulli invariant laws of finite symmetric exclusion
{c}
{title2=$\mu_\rho=\bigotimes_{x\in V}\operatorname{Bernoulli}(\rho)$}
On a finite <graph> with symmetric <edge>-swap rates, the <stirring representation of symmetric exclusion> transports the occupations by a random <permutation>. An independent identically distributed <Bernoulli distribution> occupation field is invariant under every deterministic <permutation>, and hence under this random <permutation> when it is independent of the initial field. Therefore the displayed <product measure> is invariant, including densities zero and one. Equivalently, an <edge> swap preserves the number of particles and has the same reverse rate, giving <detailed balance>.
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