Interfacing at the Stochastic Separatrix

This chapter introduces the concept of the stochastic separatrix and elaborates its application in clarifying the notion of transitions between relatively long-lived states and short-lived transition states. These may be noise-induced transitions over high barriers or the squeezing of Brownian motion through narrow necks connecting relatively large confining compartments. The stochastic separatrix plays a role in determining the dependence of the first nonzero eigenvalue of the Fokker–Planck operator (FPO) on the geometry of the drift field and on the geometry of the domain.