This is part of a virtual seminar series in theoretical condensed matter and atomic physics, with the aim to connect researchers working at different Nordic universities.
Rare and extreme events are notoriously hard to handle in any complex stochastic system: They are simultaneously too rare to be reliably observable in experiments or numerics, but at the same time often too impactful to be ignored. Large deviation theory, corresponding to a saddle-point approximation of the stochastic path integral, provides a classical way of dealing with events of extremely small probability, but generally only yields the exponential tail scaling of rare event probabilities. In this talk, I will discuss theory, and algorithms based upon it, that improve on this limitation, yielding sharp quantitative estimates of rare event probabilities from a single computation and without fitting parameters. Notably, these estimates require the computation of determinants of differential operators, which in relevant cases are not traceclass and require appropriate renormalization. We demonstrate that the Carleman-Fredholm operator determinant is the correct choice, corresponding to the renormalized fluctuation determinant around the instanton of the corresponding stochastic field theory. Throughout, I will demonstrate the applicability of these methods to high-dimensional real-world systems, for example coming from atmosphere and ocean dynamics.
Zoom-link: https://nordita.org/zoom/nvcms