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Elliptic stochastic quantisation

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SRQ - Scaling limits, rough paths, quantum field theory

I will describe the relation between elliptic SPD Es and Gibbs measures given by the dimensional reduction mechanism discovered by Parisi and Sourlas in ’79. In collaboration with S. Albeverio and F. C. De Vecchi we recently gave a rigorous proof of this relation in some particular (low dimensional) case. The proof goes via a supersymmetric representation of the law of the SPDE .




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