Random walks and diffusion

Random walks have been introduced historically in order to explain the completely random motion exhibited by pollen grains in water (the so called Brownian motion). Einstein was the first to show that this particular behaviour could be explained, in terms of random walks, as the result of the impacts of the pollen grains with water molecules: since at the time the discrete nature of matter was still not universally accepted, this was one of the first theoretical predictions of the existence of atoms and molecules, which was later proofed experimentally.