Decay of correlations in random dynamical systems
Abstract: The concept of mixing measure-preserving dynamical systems can be extended to the setting of stationary-noise-driven dynamical systems by replacing classical decay of correlation functions with almost-sure decay of "random correlation functions". In this talk, I present my current thoughts and open questions regarding the physical interpretation of this definition of mixing, particularly through examining what happens in the "trivial" case where the dynamics on the state space is described by a deterministic dynamical system independent of the realisation of the noise.
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