Quantitative homogenization on time-dependent random conductance models with stable-like jumps
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911291944206336 |
|---|---|
| author | Chen, Xin Chen, Zhen-Qing Kumagai, Takashi Wang, Jian |
| author_facet | Chen, Xin Chen, Zhen-Qing Kumagai, Takashi Wang, Jian |
| contents | We establish quantitative homogenization results for time-dependent random conductance models with stable-like long range jumps on $\Z^d$, where the transition probability from $x$ to $y$ is given by $w_{t, x,y}|x-y|^{-d-α}$ with $α\in (0,2)$. In particular, time-dependent random coefficients $\{w_{t,x,y}: t\in \R_+, (x,y)\in E\}$ are uniformly bounded from above (but may be degenerate), and satisfy the Kolmogorov continuous condition, where $E=\{(x, y): x \not= y \in \Z^d\}$ is the set of all unordered pairs on $\Z^d$. The proofs are based on $L^2$-estimates and energy estimates for solutions to regionalparabolic equations and multi-scale Poincaré inequalities associated with time-dependent symmetric stable-like random walks with random coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative homogenization on time-dependent random conductance models with stable-like jumps Chen, Xin Chen, Zhen-Qing Kumagai, Takashi Wang, Jian Probability We establish quantitative homogenization results for time-dependent random conductance models with stable-like long range jumps on $\Z^d$, where the transition probability from $x$ to $y$ is given by $w_{t, x,y}|x-y|^{-d-α}$ with $α\in (0,2)$. In particular, time-dependent random coefficients $\{w_{t,x,y}: t\in \R_+, (x,y)\in E\}$ are uniformly bounded from above (but may be degenerate), and satisfy the Kolmogorov continuous condition, where $E=\{(x, y): x \not= y \in \Z^d\}$ is the set of all unordered pairs on $\Z^d$. The proofs are based on $L^2$-estimates and energy estimates for solutions to regionalparabolic equations and multi-scale Poincaré inequalities associated with time-dependent symmetric stable-like random walks with random coefficients. |
| title | Quantitative homogenization on time-dependent random conductance models with stable-like jumps |
| topic | Probability |
| url | https://arxiv.org/abs/2511.22792 |