Stochastic Pin - Ball 3 0

A ball is propelled through a random environment of obstacles oo which it rebounds with perfect reeection. What is the behaviour of the trajectory of the ball? We summarise known mathematical results concerning this model, which we calìstochastic pin-ball', and which is known also as a `Lorentz lattice gas' and a version of which is sometimes termed thèEhrenfest wind{tree model'. The rigorous theory is more extensively developed if the environment is allowed to include a positive density of space in which the ball behaves in the manner of a random walk. For a lattice model of this type, one may employ arguments of percolation theory in order to prove theorems concerning non-localisation, transience, and asymptotic normality, under certain assumptions on the environment. 1. The origins of stochastic pin-ball There is a modern version of the game of bagatelle involving a ball which is propelled about an inclined plane and which suuers deeections as a result of collisions with protruding nails. Modern pin-ball is an electriied version of this game, with a variety of obstacles and with interaction with the player. In a simpliied stochastic model for the motion of the ball, we position smooth obstacles about R 2 at random, and we then project a ball through