Brownian motion
There are too many molecular impacts making the Brownian pattern, so no scientific model can account for all of them. That is why only probabilistic models of molecular populations can be used to describe it.  Two such models of the statistical mechanics were made by Einstein and Smoluchowski.  Another, pure probabilistic kind of models are stochastic process models.  There exist both simpler and more complicated stochastic processes which in extreme ("taken to the limit") may describe the Brownian Motion (see random walk and Donsker's theorem).