Stationary blocking measures for one-dimensional nonzero mean exclusion processes

Maury Bramson, Thomas Mountford

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


The product Bernoulli measures ρα with densities α, α ∈ [0, 1], are the extremal translation invariant stationary measures for an exclusion process with irreducible random walk kernel p(·). In d = 1, stationary measures that are not translation invariant are known to exist for specific p(·) satisfying σx xp(x) > 0. These measures are concentrated on configurations that are completely occupied by particles far enough to the right and are completely empty far enough to the left; that is, they are blocking measures. Here, we show stationary blocking measures exist for all exclusion processes in d = 1, with p(·) having finite range and σx xp(x) > 0.

Original languageEnglish (US)
Pages (from-to)1082-1130
Number of pages49
JournalAnnals of Probability
Issue number3
StatePublished - Jul 2002


  • Blocking measures
  • Exclusion processes
  • Stationary measures


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