Rare events in stochastic partial differential equations on large spatial domains

Eric Vanden Eijnden, Maria G. Westdickenberg

Research output: Contribution to journalArticle

Abstract

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
Volume131
Issue number6
DOIs
StatePublished - Jun 2008

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Rare Events
Stochastic Partial Differential Equations
partial differential equations
Large Deviation Theory
methodology
deviation
Methodology
Growth Model
Nucleation
Deduce
Subsystem
Partial differential equation
Likely
Entropy
nucleation
entropy
Model

Keywords

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

ASJC Scopus subject areas

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

Cite this

Rare events in stochastic partial differential equations on large spatial domains. / Vanden Eijnden, Eric; Westdickenberg, Maria G.

In: Journal of Statistical Physics, Vol. 131, No. 6, 06.2008, p. 1023-1038.

Research output: Contribution to journalArticle

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