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- W2965795241 abstract "We consider stochastic PDEs on the $d$-dimensional torus with fractional Laplacian of parameter $rhoin(0,2]$, quadratic nonlinearity and driven by space-time white noise. These equations are known to be locally subcritical, and thus amenable to the theory of regularity structures, if and only if $rho > d/3$. Using a series of recent results by the second named author, A. Chandra, I. Chevyrev, M. Hairer and L. Zambotti, we obtain precise asymptotics on the renormalisation counterterms as the mollification parameter $varepsilon$ becomes small and $rho$ approaches its critical value. In particular, we show that the counterterms behave like a negative power of $varepsilon$ if $varepsilon$ is superexponentially small in $(rho-d/3)$, and are otherwise of order $log(varepsilon^{-1})$. This work also serves as an illustration of the general theory of BPHZ renormalisation in a relatively simple situation." @default.
- W2965795241 created "2019-08-13" @default.
- W2965795241 creator A5022009290 @default.
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- W2965795241 date "2021-02-26" @default.
- W2965795241 modified "2023-09-25" @default.
- W2965795241 title "BPHZ renormalisation and vanishing subcriticality asymptotics of the fractional $Phi^3_d$ model" @default.
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