Hydrodynamics for the partial exclusion process in random environment

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

Asymptotic shape for the contact process in random environment

Large deviations for the contact process in random environment

The asymptotic shape theorem for the contact process in random environment gives the existence of a norm μ on R such that the hitting time t(x) is asymptotically equivalent to μ(x) when the contact process survives. We provide here exponential upper bounds for the probability of the event { t(x) μ(x) 6∈ [1 − ε, 1 + ε]}; these bounds are optimal for independent random environment. As a special c...

A limit process for partial match queries in random quadtrees

We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the classical model where the data consist of independent and uniform points in the unit square. For this model, in a structure on n points, it is known that the complexity, measured as the number of nodes Cn(ξ) to visit in order to report the items ...

Moderate Deviations for a Diffusion Type Process in Random Environment

Let σ(u), u ∈ R be an ergodic stationary Markov chain, taking a finite number of values a1, . . . , am, and b(u) = g(σ(u)), where g is a bounded and measurable function. We consider the diffusion type process dX t = b(X ε t /ε)dt+ ε σ `