User:Tkojar/sandbox

Martin Hairer's theory of regularity structures provides a framework for studying a large class of subcritical parabolic stochastic partial differential equations arising from quantum field theory. The framework covers the Kardar–Parisi–Zhang equation, the $$ \Phi_3^4$$ equation and the parabolic Anderson model, all of which require renormalization in order to have a well-defined notion of solution.

A main result of that theory is the Reconstruction theorem. Among other things, it is used in to prove Schauder estimates which in turn give the existence of the fixed point.