Large Deviations and Metastability Analysis for Heavy-Tailed Dynamical Systems

We study large deviations and metastability of heavy-tailed stochastic dynamical systems and provide the heavy-tailed counterparts of the classical Freidlin-Wentzell and Eyring-Kramers theory. Our findings address the rare-event analysis for sufficiently general events and heavy-tailed dynamical systems. We also unveil an intricate phase transitions in the first exit problems under truncated heavytailed noises. Furthermore, our results provide tools to systematically study the connection between the global dynamics of the stochastic gradient descent (SGD) under heavy-tailed noises and the generalization mystery of deep learning.