"BROWNIAN MOTION --A random movement of pollen grains suspended in water was observed by botanist Robert Brown in 1827. He thought that the movement must be due to the live pollen, but on observing (obviously) dead dye particles in water, he saw the same random dance. This motion was explained a generation later by Maxwell and Einstein. It's due to the invisible water molecules hitting the visible particle and moving it a bit. Since the particle is hit continuously from all sides, it moves in a random fashion." Quoted from Exploratorium Web site.

Brownian Motion is the incessant, erratic movement of microscopic particles suspended in a fluid (liquid or gas). Robert Brown, a British botanist, described this motion in 1827. Moving molecules strike the suspended particles at random. Albert Einstein developed a mathematical explanation of the phenomenon in 1905.

An estimate of Avogadro's Number (made by Jean Baptiste Perrin) came from a study of the Brownian motion.

Those textbook definitions do not address the issue of randomness. As a result of random collisions, where there exists a momentary imbalance due to more or stronger collisions from small surrounding particles, the larger particle moves. This motion is described using the term random walk.