R.Jack (2019) Large deviations and optimal control in growing systems, and other simple models

We consider dynamical fluctuations in a simple model where clusters of particles grow with time [1]. There are two types of particle (for example, red and blue) and the typical long-time
behaviour may be either mixed or de-mixed. We analyse rare events where the cluster composition at long times differs from its typical value [2]. The mechanisms for these events are unusual – they are coupled to large fluctuations in the early-time behaviour of the system, which impacts the long-term behaviour because of a long-range memory effect. We explain how these can be described by combining large deviatio n theory with ideas of stochastic optimal control. We discuss connections to simple models of diffusion with memory.

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