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Noncommutative Regularity Structures
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Noncommutative Regularity Structures
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We extend the theory of regularity structures [Hai14] to allow processes belonging to locally $m$-convex topological algebras. This extension includes processes in the locally $C^{*}$-algebras of [CHP25] used to localise singular stochastic partial differential equations involving fermions, as well as processes in Banach algebras such as infinite-dimensional semicircular\circular Brownian motion, and more generally the $q$-Gaussians of [BS91, BKS97, Bo\.z99]. A new challenge we encounter in the $q$-Gaussian setting with $q \in (-1,1)$ are noncommutative renormalisation estimates where we must estimate operators in homogeneous $q$-Gaussian chaoses with arbitrary operator insertions. We introduce a new Banach algebra norm on $q$-Gaussian operators that allows us to control such insertions; we believe this construction could be of independent interest.
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Cited by 1 Pith paper
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A PDE approach to the 2D Yang-Mills measure
The 2D Yang–Mills measure on the unit square admits a Coulomb-gauge representative in every Ω^1_β, β<1 — Gaussian-free-field regularity — with L^p moments growing like p^{(2+β)/2+δ}.
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