Special Session 92: Numerical Methods for SPDEs: Bridging Theory and Applications

Using Feynman diagrams in renormalisation, some new results
Nils Berglund
IDP, University of Orleans
France
Co-Author(s):    
Abstract:
We present new techniques that simplify the combinatorics of Feynman diagrams when renormalising singular SPDEs and computing expectations under their invariant measures. The techniques make use of algebraic methods, in particular a so-called Wick map. We illustrate these methods in the case of the $\Phi^4_d$ model for any, possibly non-integer dimension strictly less than $4$. Reference: https://arxiv.org/abs/2507.03820