Abstract

I will give a gentle introduction to the effects of long-range temporal correlations in stochastic particle systems, focusing particularly on fluctuations about the typical behaviour. Specifically, I will explain how long-range memory dependence can modify the large deviation principle describing the probability of rare currents and lead, for example, to superdiffusive behaviour. I will also discuss more briefly the effects of hidden states, and the implementation of the “cloning” procedure for evaluation of large deviations in non-Markovian processes. Finally, I also hope to mention a more interdisciplinary project incorporating the psychological “peak-end” heuristic for human memory into a simple discrete choice model from economics.