Rare events in stochastic partial differential equations on large spatial domains

Eric Vanden-Eijnden, Maria G. Westdickenberg

Research output: Contribution to journalArticlepeer-review


A methodology is proposed for studying rare events in stochastic partial differential equations in systems that are so large that standard large deviation theory does not apply. The idea is to deduce the behavior of the original model by breaking the system into appropriately scaled subsystems that are sufficiently small for large deviation theory to apply but sufficiently large to be asymptotically independent from one another. The methodology is illustrated in the context of a simple one-dimensional stochastic partial differential equation. The application reveals a connection between the dynamics of the partial differential equation and the classical Johnson-Mehl-Avrami- Kolmogorov nucleation and growth model. It also illustrates that rare events are much more likely and predictable in large systems than in small ones due to the extra entropy provided by space.

Original languageEnglish (US)
Pages (from-to)1023-1038
Number of pages16
JournalJournal of Statistical Physics
Issue number6
StatePublished - Jun 2008


  • Large deviation theory
  • Metastability
  • Nucleation
  • Phase transformation
  • Rare events
  • Small noise
  • Spatially extended system
  • Stochastic partial differential equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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