On the space-time fluctuations of the SHE and KPZ equation in the entire $L^{2}$-regime for spatial dimensions $d \geq 3$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912549911396352 |
|---|---|
| author | Wang, Te-Chun |
| author_facet | Wang, Te-Chun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06874 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the space-time fluctuations of the SHE and KPZ equation in the entire $L^{2}$-regime for spatial dimensions $d \geq 3$ Wang, Te-Chun Probability Mathematical Physics 60K37, 60H15, 82D60 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. |
| title | On the space-time fluctuations of the SHE and KPZ equation in the entire $L^{2}$-regime for spatial dimensions $d \geq 3$ |
| topic | Probability Mathematical Physics 60K37, 60H15, 82D60 |
| url | https://arxiv.org/abs/2402.06874 |