Anomalous Slow Diffusion from Perpetual Homogenization
| dc.creator | Owhadi, Houman | |
| dc.date | 2001-05-20 | |
| dc.date | 2004-03-30 | |
| dc.date.accessioned | 2026-07-07T04:41:47Z | |
| dc.date.available | 2026-07-07T04:41:47Z | |
| dc.description | This paper is concerned with the asymptotic behavior of solutions of stochastic differential equations $dy_t=dω_t -\nabla V(y_t) dt$, $y_0=0$. When $d=1$ and $V$ is not periodic but obtained as a superposition of an infinite number of periodic potentials with geometrically increasing periods ($V(x) = \sum_{k=0}^\infty U_k(x/R_k)$, where $U_k$ are smooth functions of period 1, $U_k(0)=0$, and $R_k$ grows exponentially fast with $k$) we can show that $y_t$ has an anomalous slow behavior and we obtain quantitative estimates on the anomaly using and developing the tools of homogenization. Pointwise estimates are based on a new analytical inequality for sub-harmonic functions. When $d\geq 1$ and $V$ is periodic, quantitative estimates are obtained on the heat kernel of $y_t$, showing the rate at which homogenization takes place. The latter result proves Davies's conjecture and is based on a quantitative estimate for the Laplace transform of martingales that can be used to obtain similar results for periodic elliptic generators | |
| dc.description | Published version. Contains the full proof of Davies's conjecture | |
| dc.identifier | https://arxiv.org/abs/math/0105165 | |
| dc.identifier | http://arxiv.org/abs/math/0105165 | |
| dc.identifier | Annals of Probability, Vol. 31, No. 4 - October 2003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61502 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | Primary 60J60; secondary, 35B27, 34E13, 60G44, 60F05, 31C05 | |
| dc.title | Anomalous Slow Diffusion from Perpetual Homogenization | |
| dc.type | text |