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is now known as the Brownian web was first conceived by Arratia in his Ph.D. thesis and a subsequent incomplete and unpublished manuscript.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
Rotational Brownian motion imposed electric field. Rotational Brownian motion was first discussed by Peter Debye, who applied Einstein's theory of translational Brownian motion to the rotation of molecules having permanent electric dipoles. Debye ignored inertial effects and assumed that the molecules were spherical, with an intrinsic, fixed dipole moment. He derived expressions for the dielectric relaxation time and for the permittivity. These formulae have been successfully applied to many materials. However, Debye's expression for the permittivity predicts that the absorption tends toward a constant value when the frequency of the applied electric field becomes very large—the "Debye plateau". This is not observed; instead,