Convergence of stochastic cellular automation to Burgers' equation: Fluctuations and stability

Joel L. Lebowitz, Enza Orlandi, Errico Presutti

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We prove that for almost all realizations of the Boghosian-Levermore stochastic cellular automaton model the density profile converges, in the scaling limit, to the solution of Burgers' equation. The proof goes via the propagation of chaos and yields tight bounds on the fluctuations. These estimates also yield stability properties of the (smooth) shock front: at long times it remains well defined on a microscopic scale-but its location fluctuates.

Original languageEnglish (US)
Pages (from-to)165-188
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume33
Issue number1-3
DOIs
StatePublished - 1988

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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