Collective Motion of Interacting Random Walkers

The collective motion of a large group of individuals has two different scales. Individuals move and interact on a local scale, while the motion of the group as a whole occurs on a global scale. All the movement of the group on the global scale is produced by the many movements of its members, and so a good model for the global behaviour should arise from local models for the individuals. We investigate the link between the two scales, and create formulae for producing a global model for any particular lattice-based local model using mean-field approximations.