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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

7 votes
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Feynman-Kac formula for the GFF

The Feynman-Kac formula says that $$ \exp(-t(-\Delta+V(X)))(x,y) = \mathbb{E}_{\gamma(0)=x,\gamma(t)=y}\left[\exp(-\int_0^t V\circ\gamma)\right] $$ where $\Delta$ is the Laplacian on $L^2(\mathbb{R}^n …