We study quasi-stationary measures for conservative particle systems in the in finite lattice. Existence of quasi-stationary measures is established for a fairly general class of reversible systems. For the special cases of a system of independent random walks and the symmetric simple exclusion process, it is shown that qualitative features of quasi-stationary measures change drastically with dimension.
"Quasi-Stationary measures for conservative dynamics in the infinite lattice." Ann. Probab. 29 (4) 1733 - 1754, October 2001. https://doi.org/10.1214/aop/1015345770