Weak Universality of the Dynamical Φ34 Model on the Whole Space

Rongchan Zhu; Xiangchan Zhu

doi:10.1007/s11118-021-09941-0

Weak Universality of the Dynamical Φ34 Model on the Whole Space

Rongchan Zhu, Xiangchan Zhu^*

^*Corresponding author for this work

School of Mathematics and Statistics

CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We prove that the large scale behavior of a class of stochastic weakly nonlinear reaction-diffusion models on ℝ³ converges to the dynamical Φ34 model using paracontrolled distributions on weighted Besov spaces. Our approach depends on the delicate choice of the weight, the localization operator technique and a modified version of the maximum principle from Gubinelli and Hofmanová (Commun. Math. Phys. 368, 1201–1266, 5).

Original language	English
Pages (from-to)	295-330
Number of pages	36
Journal	Potential Analysis
Volume	58
Issue number	2
DOIs	https://doi.org/10.1007/s11118-021-09941-0
Publication status	Published - Feb 2023

Keywords

Paracontrolled distributions
Renormalisation
Space-time white noise
Weak universality
Φ model

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10.1007/s11118-021-09941-0

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abstract = "We prove that the large scale behavior of a class of stochastic weakly nonlinear reaction-diffusion models on ℝ3 converges to the dynamical Φ34 model using paracontrolled distributions on weighted Besov spaces. Our approach depends on the delicate choice of the weight, the localization operator technique and a modified version of the maximum principle from Gubinelli and Hofmanov{\'a} (Commun. Math. Phys. 368, 1201–1266, 5).",

keywords = "Paracontrolled distributions, Renormalisation, Space-time white noise, Weak universality, Φ model",

author = "Rongchan Zhu and Xiangchan Zhu",

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AB - We prove that the large scale behavior of a class of stochastic weakly nonlinear reaction-diffusion models on ℝ3 converges to the dynamical Φ34 model using paracontrolled distributions on weighted Besov spaces. Our approach depends on the delicate choice of the weight, the localization operator technique and a modified version of the maximum principle from Gubinelli and Hofmanová (Commun. Math. Phys. 368, 1201–1266, 5).

KW - Paracontrolled distributions

KW - Renormalisation

KW - Space-time white noise

KW - Weak universality

KW - Φ model

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Weak Universality of the Dynamical Φ34 Model on the Whole Space

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Keywords

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