Stochastic acceleration in a random time-dependent potential

We study the long time behaviour of the speed of a particle moving in ${\mathbb{R}}^d$ 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 $t^{\frac{2}{5}}$ when $d>5$.