Two Simulation Methods of Brownian Motion

Abstract Einstein-Smoluchowski’s theory and Langevin’s are two main theories to describe Brownian motion. The Einstein-Smoluchowski regards motion as random walking of particles, while the Langevin establishes a differential equation describing particles. Both involve numbers, i.e., only statistical results can be discussed. Based on above theories, this paper presents corresponding simulations, which verifies conclusions well compares their similarities, differences, applicable conditions. These offer guideline for further studies