Isotropic evolution process with Gauss distributed particle's position in $\mathbb{R}^{d}$

Abstract

In this work, we study an isotropic random motion of a particle whose velocity has the Maxwell--Boltzmann distribution. We give some specific results for the one-, three-, and $d$-dimensional cases. In all of them, the particle position at a given time $t$ is normal- or Gauss-distributed.