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- W3006310000 abstract "We construct solutions of a renormalized continuum fractional parabolic Anderson model, formally given by $partial _{t}u=-(-Delta )^{frac {1}{2}}u+xi u$, where $xi $ is a periodic spatial white noise. To be precise, we construct limits as $varepsilon to 0$ of solutions of $partial _{t}u_{varepsilon }=-(-Delta )^{frac {1}{2}}u_{varepsilon }+(xi _{varepsilon }-C_{varepsilon })u_{varepsilon }$, where $xi _{varepsilon }$ is a mollification of $xi $ at scale $varepsilon $ and $C_{varepsilon }$ is a logarithmically diverging renormalization constant. We use a simple renormalization scheme based on that of Hairer and Labbé, “A simple construction of the continuum parabolic Anderson model on $mathbf {R}^{2}$.”" @default.
- W3006310000 created "2020-02-24" @default.
- W3006310000 creator A5090427336 @default.
- W3006310000 date "2020-01-01" @default.
- W3006310000 modified "2023-10-14" @default.
- W3006310000 title "The continuum parabolic Anderson model with a half-Laplacian and periodic noise" @default.
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- W3006310000 doi "https://doi.org/10.1214/20-ecp342" @default.
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