Statistical Description of Contact-Interacting Brownian Walkers on the Line

Ibrahim Fatkullin, Eric Vanden Eijnden

Research output: Contribution to journalArticle

Abstract

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
Volume112
Issue number1-2
DOIs
StatePublished - Jul 2003

Fingerprint

Contact
intervals
Interval
Line
Collision
Statistical Independence
Voter Model
collisions
Scaling Limit
Approximation
probability density functions
approximation
direct numerical simulation
Probability density function
scaling
expansion
Series
Context
Direct numerical Simulation

Keywords

  • Brownian walkers
  • Diffusion-limited reactions
  • Voter model

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Statistical Description of Contact-Interacting Brownian Walkers on the Line. / Fatkullin, Ibrahim; Vanden Eijnden, Eric.

In: Journal of Statistical Physics, Vol. 112, No. 1-2, 07.2003, p. 155-163.

Research output: Contribution to journalArticle

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