Article,
Rare Events in Stochastic Partial Differential Equations on Large Spatial Domains
Journal of Statistical Physics, 131 (6): 1023--1038 (June 2008)
Abstract
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 breakingthe system into appropriately scaled subsystems that are sufficiently small for large deviation theory to apply but sufficientlylarge to be asymptotically independent from one another. The methodology is illustrated in the context of a simple one-dimensionalstochastic partial differential equation. The application reveals a connection between the dynamics of the partial differentialequation and the classical Johnson–Mehl–Avrami–Kolmogorov nucleation and growth model. It also illustrates that rare eventsare much more likely and predictable in large systems than in small ones due to the extra entropy provided by space.
