Iterated scaling limits for aggregation of random coefficient AR(1) and INAR(1) processes

Scaling limits for symmetric Itô-Lévy processes in random medium

Abstract We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit exhibits a diffusive or superdiffusive behavior, depending on the integrability properties of the Poisson random measure.

Scaling Limits for Cumulative Input Processes

We study different scaling behavior of very general telecommunications cumulative input processes. The activities of a telecommunication system are described by a marked-point process Tn Zn n∈ , where Tn is the arrival time of a packet brought to the system or the starting time of the activity of an individual source, and the mark Zn is the amount of work brought to the system at time Tn. This ...

Random fractals and scaling limits in percolation

Scaling limits of large random trees

The goal of these lectures is to survey some of the recent progress on the description of largescale structure of random trees. We will use the framework of Markov branching sequences of trees and develop several applications, to combinatorial trees, Galton-Watson trees, some dynamical models of randomly growing trees, cut trees, etc. This is a rough draft – to be completed – all comments are w...

Scaling Limits for Internal Aggregation Models with Multiple Sources

We study the scaling limits of three different aggregation models on Z: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, al...