This paper concerns the homogenization problem of a parabolic equation with large, timedependent, random potentials in high dimensions d ≥ 3. Depending on the competition between temporal and spatial mixing of the randomness, the homogenization procedure turns to be different. We characterize the difference by proving the corresponding weak convergence of Brownian motion in random scenery. When...

Particulate Matter (PM) is a form of air pollution that visually degrades urban scenery and is hazardous to human health and the environment. Current monitoring devices are limited in measuring average PM over large areas. Quantifying the visual effects of haze in digital images of urban scenery and correlating these effects to PM levels is a vital step in more practically monitoring our enviro...

Completing previous results, we construct, for every 1/2 6 s 6 1, explicit examples of nearest neighbour random walks on the nonnegative integer line such that s is the scaling exponent of the associated random walk in random scenery for square integrable i.i.d. sceneries. We use coupling techniques to compare the distributions of the local times of such random walks.

Kalikow (1982) proved that the [T, T−1] transformation is not isomorphic to a Bernoulli shift. We show that the scenery factor of the [T,T−1] transformation is not isomorphic to a Bernoulli shift. Moreover, we show that it is not Kakutani equivalent to a Bernoulli shift.