Convolution calculus on white noise spaces and Feynman graph representation of generalized renormalization flows

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In this note we outline some novel connections between the following fields: 1) Convolution calculus on white noise spaces 2) Pseudo-differential operators and Lévy processes on infinite dimensional spaces 3) Feynman graph representations of convolution semigroups 4) generalized renormalization group flows and 5) the thermodynamic limit of particle systems.