We study the long time behaviour of the speed of a particle moving in R d under the influence of a random time-dependent potential representing the particle's environment. The particle undergoes successive scattering events that we model with a Markov chain for which each step represents a collision. Assuming the initial velocity is large enough, we show that, with high probability, the particle's kinetic energy E(t) grows as t

Abstract-The number of connected devices is growing and in the near future it is expected to become extremely large in cities. As a consequence, using simulators to study and prepare a project of installing new networks before their real deployment is of great importance. They can help to predict some important information like signal overload or the feasibility of the deployment in terms of location, interferences, communication and cost. In this paper we present a new architecture for the platform CupCarbon, developed within the research project PERSEPTEUR. The main objective of this platform is to design and simulate Wireless Sensor Networks dedicated to Smart-city and IoT applications. It allows to validate distributed algorithms in a 2D/3D environment, taking account of the city buildings in which to deploy the network, the mobiles, and using accurate models of radio propagation and interferences in that environment.

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