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is now known as the Brownian web was first conceived by Arratia in his Ph.D. thesis and a subsequent incomplete and unpublished manuscript.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 square root of the total population. Suppose that a Brownian particle of mass "M" is surrounded by lighter particles of mass "m" which are traveling at a speed "u". Then, reasons Smoluchowski, in any collision between a surrounding and Brownian particles, the velocity transmitted to the latter will be "mu"/"M". This ratio is of the order of 10 cm/s. But we also have to take into consideration that in a gas there will be more than 10 collisions in a second, and even greater in a liquid where we expect that there will be 10 collision in one second. Some