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The $\Phi_3^4$ measure has sub-Gaussian tails

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arxiv 2102.11685 v2 pith:FU4ACTDE submitted 2021-02-23 math.PR math-phmath.MP

Martin Hairer , Rhys Steele This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords measuresimpletailsargumentcorrespondingexpectedexponentialexpression
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abstract

We provide a very simple argument showing that the $\Phi^4_3$ measure does have quartic exponential tails, as expected from its formal expression. This shows that the corresponding moment problem is well-posed and provides a simple path to observing non-Gaussianity of the measure.

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  1. Noncommutative Regularity Structures

    math.PR 2025-09 conditional novelty 8.0 of 10

    Noncommutative regularity structures: a general theory for singular SPDEs with values in locally m-convex algebras, applied to q-Gaussian, fermionic, and mixed boson-fermion noises.

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