The Point of View of the Particle on the Law of Large Numbers for Random Walks in a Mixing Random Environment

The point of view of the particle is an approach that has proven very powerful in the study of many models of random motions in random media. We provide a new use of this approach to prove the law of large numbers in the case of one or higher-dimensional, finite range, transient random walks in mixing random environments. One of the advantages of this method over what has been used so far is that it is not restricted to i.i.d. environments.Comment: 22 pages. To appear in the Annals of Probabilit

The Political Economy of Disaster Vulnerability: A Case Study of Pakistan Earthquake 2005

Literature on natural hazards typically perceives disasters to be acts of God (or nature) while restricting the examination of their causes to biophysical and geographical explanations. This paper takes a different approach; first, it argues that disasters are socially constructed and, second, it situates the interactions of large-scale natural forces with local political-economic conditions within the context of vulnerability to contend that disasters are consequences of unresolved development challenges. Using the Pressure and Release (PAR) Model the paper suggests the usefulness of the concept of vulnerability that shapes local geographies of risk and weak institutions which transform and enhance the negative impacts of ‘natural’ hazards into ‘man-made’ disasters.Vulnerability, Natural Hazards, Disasters, Political Economy, Pakistan

Almost sure functional central limit theorem for non-nestling random walk in random environment

We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost every environment for the centered and diffusively scaled walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.Comment: 54 pages. Small edits in tex

Process-level quenched large deviations for random walk in random environment

We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative entropy.Comment: Proof of (6.2) corrected. Lemma A.2 replace