Anomalous Slow Diffusion from Perpetual Homogenization

Details Anomalous Slow Diffusion from Perpetual Homogenization Anomalous Slow Diffusion from Perpetual Homogenization

2001-05-20

arxiv.org/abs/math/0105165v2

Annals of Probability, Vol. 31, No. 4 - October 2003

Mathematics

Probability

Published version. Contains the full proof of Davies's conjecture

Scientific paper

This paper is concerned with the asymptotic behavior of solutions of stochastic differential equations $dy_t=d\omega_t -\nabla V(y_t) dt$, $y_0=0$. 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

Affiliated with

Also associated with

No associations

Rating

Anomalous Slow Diffusion from Perpetual Homogenization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Anomalous Slow Diffusion from Perpetual Homogenization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Anomalous Slow Diffusion from Perpetual Homogenization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-470785