Diffusion, peer pressure and tailed distributions

Abstract

We present a general, physically motivated non-linear and non-local advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an integrable dynamical system, that on varying a parameter, the steady state behaviour undergoes a transition from the standard diffusive behavior to a localized stationary state characterized by a tailed distribution. Finally, we show that recent empirical laws on economic growth can be explained as a collective phenomenon due to peer pressure interaction.Comment: RevTex: 4 pages + 3 eps-figures. Minor Revision and figure 3 replaced. To appear in Phys. Rev. Letter