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<p>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 <i>N</i> walkers confirm these analytic predictions in the large-<i>N</i> 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.</p>

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

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  • 发表日期：

    2026年3月14日

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  • A. C. Maggs

摘要

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.