The heat equation with time-correlated random potential in d=2: Edwards-Wilkinson fluctuations
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916569233227776 |
|---|---|
| author | Kotitsas, Sotirios |
| author_facet | Kotitsas, Sotirios |
| contents | We consider the stochastic PDE:
$\partial_tu(t,x)=\frac{1}{2}Δu(t,x)+β{}u(t,x)V(t,x),$
in dimension $d=2$, where the potential V is the space and time mollification of the two-dimensional space-time white noise. We show that after renormalizing, the fluctuations of the solution converge to the Edwards-Wilkinson limit with an explicit effective variance and constant effective diffusivity. Our main tool is a Markov chain on the space of paths which we use to establish an extension of the Kallianpur-Robbins law to a specific regenerative process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01519 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The heat equation with time-correlated random potential in d=2: Edwards-Wilkinson fluctuations Kotitsas, Sotirios Probability We consider the stochastic PDE: $\partial_tu(t,x)=\frac{1}{2}Δu(t,x)+β{}u(t,x)V(t,x),$ in dimension $d=2$, where the potential V is the space and time mollification of the two-dimensional space-time white noise. We show that after renormalizing, the fluctuations of the solution converge to the Edwards-Wilkinson limit with an explicit effective variance and constant effective diffusivity. Our main tool is a Markov chain on the space of paths which we use to establish an extension of the Kallianpur-Robbins law to a specific regenerative process. |
| title | The heat equation with time-correlated random potential in d=2: Edwards-Wilkinson fluctuations |
| topic | Probability |
| url | https://arxiv.org/abs/2405.01519 |