Brownian web Brownian web In probability theory, the Brownian web is an uncountable collection of one-dimensional coalescing Brownian motions, starting from every point in space and time. It arises as the diffusive space-time scaling limit of a collection of coalescing random walks, with one walk starting from each point of the integer lattice Z at each time. What is now known as the Brownian web was first conceived by Arratia in his Ph.D. thesis and a subsequent incomplete and unpublished manuscript. Arratia studied the voter model, an interacting particle system that models the evolution of a population's political opinions. The individuals of
Brownian motion mingling motion of dust particles is caused largely by air currents, the glittering, tumbling motion of small dust particles is, indeed, caused chiefly by true Brownian dynamics. While Jan Ingenhousz described the irregular motion of coal dust particles on the surface of alcohol in 1785, the discovery of this phenomenon is often credited to the botanist Robert Brown in 1827. Brown was studying pollen grains of the plant "Clarkia pulchella" suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of inorganic matter he