The Brownian Conga Line

Abstract

We introduce a new model called the Brownian Conga Line. It is a random curve evolving in time, generated when a particle performing a two dimensional Gaussian random walk leads a long chain of particles connected to each other by cohesive forces. We approximate the discrete Conga line in some sense by a smooth random curve and subsequently study some properties of this smooth curve. Some such properties include the different scales in which particles show noticeable motion in different regions of the Conga line, distribution of critical points, length, and distribution of loops.

arXiv comment53 pages, 5 figures. To appear in Probab. Theory and Rel. Fields