Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flow equation approach to singular stochastic PDEs   We prove universality of a macroscopic behavior of solutions of a large class
of semi-linear parabolic SPDEs on $\mathbb{R}_+\times\mathbb{T}$ with
fractional Laplacian $(-\Delta)^{\sigma/2}$, additive noise and polynomial
non-linearity, where $\mathbb{T}$ is the $d$-dimensional torus. We consider the
weakly non-linear regime and not necessarily Gaussian noises which are
stationary, centered, sufficiently regular and satisfy some integrability and
mixing conditions. We prove that the macroscopic scaling limit exists and has a
universal law characterized by parameters of the relevant perturbations of the
linear equation. We develop a new solution theory for singular SPDEs of the
above-mentioned form using the Wilsonian renormalization group theory and the
Polchinski flow equation. In particular, in the case of $d=4$ and the cubic
non-linearity our analysis covers the whole sub-critical regime $\sigma>2$. Our
technique avoids completely all the algebraic and combinatorial problems
arising in different approaches.

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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin