Brownian motion is the stochastic, irregular movement of microscopic particles suspended in a fluid, arising from incessant bombardment by thermally agitated solvent molecules. Phenomenologically, it is modeled as a continuous-time random walk with independent, normally distributed increments and stationary variance proportional to time, and in the limit as time steps go to zero, it is described by a Wiener process. As a physical phenomenon, Brownian motion underlies diffusion, is characterized quantitatively by the diffusion coefficient via the Einstein relation, and plays a fundamental role in nonequilibrium statistical mechanics and fluctuation phenomena in condensed matter systems.
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