Abstract
Studies a nonlinear heat equation in a finite interval of space subject to a white noise forcing term. The equation without the forcing term exhibits several equilibrium configurations, two of which are stable. The solution of the complete forced equation is a stochastic process in space and time that has a unique stochastic equilibrium. The authors study this process in the limit of small noise, and obtain lower and upper bounds for the probability of large fluctuations. They then apply these estimates to calculate the transition probability between the stable configurations (tunnelling). This model problem can be interpreted as a rigorous version of some recent attempts to describe Euclidean quantum systems in terms of stochastic equilibrium states of a nonlinear stochastic differential equation in infinite dimensions. However, its significance goes beyond this situation and the authors' methods may be applicable to models in other areas of natural science.
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