Flow equation approach to singular stochastic PDEs

Abstract: Most stochastic PDEs arising in physics, such as the KPZ equation describing the motion of a growing interface or the stochastic quantization equation of the $\Phi^4$ Euclidean QFT, are ill-posed in the classical analytic sense due to irregular nature of random terms. Equations of this type are called singular. Regularization and renormalization are usually necessary to give mathematical meaning to such equations. In the talk, I will present a novel technique of solving singular stochastic PDEs. The technique is based on the renormalization group flow equation. It is applicable to a large class of parabolic or elliptic SPDEs with fractional Laplacian, additive noise and polynomial non-linearity. It covers equations in the whole super-renormalizable regime. A nice feature of the method is that it avoids the algebraic and combinatorial problems arising in different approaches. Based on arXiv:2109.11380 and arXiv:2201.05031.

mathematical physics

Audience: researchers in the discipline

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