Brownian web paths from a random space time point. The introduction of this topology allowed them to prove the convergence of the coalescing random walks to a unique limiting object and characterize it. They named this limiting object Brownian web. An extension of the Brownian web, called the Brownian net, has been introduced by Sun and Swart by allowing the coalescing Brownian motions to undergo branching. An alternative construction of the Brownian net was given by Newman, Ravishankar and Schertzer. For a recent survey, see Schertzer, Sun and Swart. Brownian web In probability theory, the Brownian web is an uncountable collection of
Brownian motion mass of a mole of the gas by Avogadro's constant. The first part of Einstein's argument was to determine how far a Brownian particle travels in a given time interval. Classical mechanics is unable to determine this distance because of the enormous number of bombardments a Brownian particle will undergo, roughly of the order of 10 collisions per second. Thus Einstein was led to consider the collective motion of Brownian particles. He regarded the increment of particle positions in time formula_1 in a one dimensional ("x") space (with the coordinates chosen so that the origin lies at the initial position