Brownian Motion

Brownian motion or pedesis (from Greek: πήδησις Pɛɖeːsɪs "leaping") is the presumably random moving of particles suspended in a fluid (a liquid or a gas) resulting from their bombardment by the fast-moving atoms or molecules in the gas or liquid. The term "Brownian motion" can also refer to the mathematical model used to describe such random movements, which is often called a particle theory.

In 1827 the biologist Robert Brown, looking through a microscope at pollen grains in water, noted that the grains moved through the water but was not able to determine the mechanisms that caused this motion. The direction of the force of atomic bombardment is constantly changing, and at different times the pollen grain is hit more on one side than another, leading to the seemingly random nature of the motion. This type of phenomenon is named in Brown's honor.

The mathematical model of Brownian motion has several real-world applications. Stock market fluctuations are often cited, although Benoit Mandelbrot rejected its applicability to stock price movements in part because these are discontinuous.

Brownian motion is among the simplest of the continuous-time stochastic (or probabilistic) processes, and it is a limit of both simpler and more complicated stochastic processes (see random walk and Donsker's theorem). This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience rather than the accuracy of the models that motivates their use. This is because Brownian motion, whose time derivative is everywhere infinite, is an idealised approximation to actual random physical processes, which always have a finite time scale.