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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The study of return-times and hitting-times of small sets ("rare events") in ergodic dynamical systems has undergone some intense research in the past 20 years. It is part of the wider field of probabilistic properties of (deterministic) dynamical systems. One general motivation from the sciences is that the times at which various extreme events (possibly modeling catastrophes in real-world systems) occur, often cannot be predicted over a reasonably long period. It is therefore important to at least understand the statistical laws governing these occurrences. Accordingly, there are well-developed stochastic models describing such rare events and enabling further theoretical analysis. These stochastic descriptions, however, necessarily start from simplifying assumptions and sometimes disregard additional detailed knowledge about the mechanisms driving the system. In contrast, there is a branch of ergodic theory which aims at analysing dynamical system models which incorporate this extra information, and rigorously derives statistical properties from the underlying deterministic dynamics. The central theme of this workshop is the aspiration for finding and proving probabilistic limit theorems which clarify patterns of occurrences of extreme events in nonlinear dynamics.

Complex Systems, Chaos and Self-Organisation,    Probability and Statistics, Game Theory