Dynamics of a Bricklayer Model: Multi-Walker Realizations of True Self-Avoiding Motion

Abstract We investigate a multi-walker generalization of the true self-avoiding walk, formulated as a bricklayer model where agents collectively build a growing interface. We investigate the coupled partial differential equations that describe the hydrodynamic limit of this process. Stochastic simulations of N walkers confirm these analytic predictions in the large- N limit, revealing a characteristic parabolic density profile. These results provide a continuum description for the dynamics of non-reversible Monte Carlo algorithms, offering insights into the relaxation mechanisms of collective sampling schemes.