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| It is now well understood that there is a strong connection between gradient flows on one hand and large-deviation principles on the other hand. In a sense, this connection takes the form of a single functional that characterizes both the large deviations and the gradient-flow behaviour.
In this talk, which is work with Giovanni Bonaschi and Giuseppe Savare', I will show how this insight produces a unification of both structure and method. I will focus on a very simple stochastic system, and show how the large-deviation rate functional is related to a generalized gradient flow - with a parameter. By taking various limits in this parameter we recover both linear gradient-flow behaviour and rate-independent behaviour.
The unification lies in the fact that we can base our entire discussion on this one functional. It characterizes the structure and is also the main actor in the limit-taking, leading both to compactness and to characterization of the limit. This work shows how the connection between large deviations and gradient flows is not only philosophically interesting but also provides tools for analysis. |
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