Spatial structure in diffusion-limited two-particle reactions

Maury Bramson, Joel L. Lebowitz

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We analyze the limiting behavior of the densities ρA(t) and ρB(t), and the random spatial structure ξ(r) = (ξA(t)., ξB(t)), for the diffusion-controlled chemical reaction A+B→inert. For equal initial densities ρB(0) = ρb(0) there is a change in behavior from d≤ 4, where ρA(t) =ρB(t) ≈C/td/4, to d ≥ 4, where ρA(t) =ρb(t) ≈C/t as t → ∞; the term C depends on the initial densities and changes with d. There is a corresponding change in the spatial structure. In d < 4, the particle types separate with only one type present locally, and ξ, after suitable rescaling, tends to a random Gaussian process. In d >4, both particle types are, after large times, present locally in concentrations not depending on type or location. In d=4, both particle types are present locally, but with random concentrations, and the process tends to a limit.

Original languageEnglish (US)
Pages (from-to)941-951
Number of pages11
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Dec 1 1991


  • Diffusion-limited reaction
  • annihilating random walks
  • asymptotic densities
  • exact results
  • spatial structure


Dive into the research topics of 'Spatial structure in diffusion-limited two-particle reactions'. Together they form a unique fingerprint.

Cite this