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Construction of $\Phi^4_3$ diagrams for pedestrians

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arxiv 1610.08897 v2 pith:XTHNTKK5 submitted 2016-10-27 math.PR math-phmath.MP

Jean-Christophe Mourrat , Hendrik Weber , Weijun Xu This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords constructionobjectsstochasticappearingdescribingdiagramsdynamicalemphasis
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abstract

We aim to give a pedagogic and essentially self-contained presentation of the construction of various stochastic objects appearing in the dynamical $\Phi^4_3$ model. The construction presented here is based on the use of paraproducts. The emphasis is on describing the stochastic objects themselves rather than introducing a solution theory for the equation.

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  1. Lecture notes on the flow equation approach to singular stochastic PDEs

    math.PR 2025-11 conditional novelty 4.0 of 10

    A scale-by-scale flow equation with suitably chosen counterterms constructs renormalized solutions of fractional elliptic Phi^4 SPDEs throughout the subcritical regime.

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