On random walks in random scenery

This paper considers 1-dimensional generalized random walks in random scenery. That is, the steps of the walk are generated by an arbitrary stationary process, and also the scenery is a priori arbitrary stationary. Under an ergodicity condition--which is satisfied in the classical case--a simple proof of the distinguishability of periodic sceneries is given.Comment: Published at http://dx.doi.org/10.1214/074921706000000068 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The geometry of fractal percolation

A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation. The extensions go in three directions: {itemize} the statements work for all directions, not almost all, the statements are true for more general projections, for example radial projections onto a circle, in the case $\dim_H >1$, each projection has not only positive Lebesgue measure but also has nonempty interior. {itemize}Comment: Survey submitted for AFRT2012 conferenc

P\'olya number of continuous-time quantum walks

We propose a definition for the P\'olya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their P\'olya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.Comment: 8 pages, no figures. Accepted for publication in Physical Review

Detection of contaminant plumes released from landfills

International audienceContaminant leaks released from landfills are a significant threat to groundwater quality. The groundwater detection monitoring systems installed in the vicinity of such facilities are vital. In this study the detection probability of a contaminant plume released from a landfill has been investigated by means of both a simulation and an analytical model for both homogeneous and heterogeneous aquifer conditions. The results of the two models are compared for homogeneous aquifer conditions to illustrate the errors that might be encountered with the simulation model. For heterogeneous aquifer conditions contaminant transport is modelled by an analytical model using effective (macro) dispersivities. The results of the analysis show that the simulation model gives the concentration values correctly over most of the plume length for homogeneous aquifer conditions, and that the detection probability of a contaminant plume at given monitoring well locations match quite well. For heterogeneous aquifer conditions the approximating analytical model based on effective (macro) dispersivities yields the average concentration distribution satisfactorily. However, it is insufficient in monitoring system design since the discrepancy between the detection probabilities of contaminant plumes at given monitoring well locations computed by the two models is significant, particularly with high dispersivity and heterogeneity