Statistical Description of Contact-Interacting Brownian Walkers on the Line

Ibrahim Fatkullin, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


The distribution of interval lengths between Brownian walkers on the line is investigated. The walkers are independent until collision; at collision, the left walker disappears, and the right walker survives with probability p. This problem arises in the context of diffusion-limited reactions and also in the scaling limit of the voter model. A systematic expansion in correlation between neighbor intervals gives a series of approximations of increasing accuracy for the probability density functions of interval lengths. The first approximation beyond mere statistical independence between successive intervals already gives excellent results, as established by comparison with direct numerical simulations.

Original languageEnglish (US)
Pages (from-to)155-163
Number of pages9
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Jul 2003


  • Brownian walkers
  • Diffusion-limited reactions
  • Voter model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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