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arXiv · 2410.12373

Random sequential covering of a one-dimensional lattice by $k$-mers

Pascal Viot·P. L. Krapivsky
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Abstract

In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts that increase coverage are accepted. The process continues indefinitely on an infinite substrate, and we analyze the dynamics of random sequential covering of $\mathbb{Z}$ using $k$-mers. We introduce a method that provides a comprehensive solution to the dynamics of this process. We derive explicit solutions for trimers, tetramers, and pentamers; we study numerically random sequential covering by longer polymers ($k>5$).

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Pascal Viot, P. L. Krapivsky. 2024-10-16. Random sequential covering of a one-dimensional lattice by $k$-mers. https://doi.org/10.1088/1742-5468%2Fad930b

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