Dynamics of a bricklayer model: multi-walker realizations of true self-avoiding motion

We consider a multi-walker generalization of the true self-avoiding walk: the bricklayer model. We perform stochastic simulations, and solve the partial differential equations that describe the collective motion of $N$ bricklayers/walkers coupled to the contour of an expanding wall. In the large-$N$ limit, the results from simulation agree with the solution of the partial differential equations.