On the space-time fluctuations of the SHE and KPZ equation in the entire $L^{2}$-regime for spatial dimensions $d \geq 3$

Te-Chun Wang

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arXiv · 2402.06874

On the space-time fluctuations of the SHE and KPZ equation in the entire $L^{2}$-regime for spatial dimensions $d \geq 3$

Te-Chun Wang

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Abstract

We consider the mollified versions of the Kardar-Parisi-Zhang (KPZ) equation and the stochastic heat equation (SHE) in high dimensions $d\geq 3$ and analyze their probability distributions as the mollification is removed. Up to the $L^2$-criticality, we prove Gaussian limits, possibly with random perturbations, for the space-time fluctuations of the mollified versions around their stationarity. This result establishes a continuous analogue of the discrete case obtained by Cosco and Nakajima (2021), and further extends it to a multi-point framework.

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BibTeX RIS

Te-Chun Wang. 2024-02-10. On the space-time fluctuations of the SHE and KPZ equation in the entire $L^{2}$-regime for spatial dimensions $d \geq 3$. https://arxiv.org/abs/2402.06874

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