Exact Solution of a Drop-push Model for Percolation
<|reference_start|>Exact Solution of a Drop-push Model for Percolation: Motivated by a computer science algorithm known as `linear probing with hashing' we study a new type of percolation model whose basic features include a sequential `dropping' of particles on a substrate followed by their transport via a `pushing' mechanism. Our exact solution in one dimension shows that, unlike the ordinary random percolation model, the drop-push model has nontrivial spatial correlations generated by the dynamics itself. The critical exponents in the drop-push model are also different from that of the ordinary percolation. The relevance of our results to computer science is pointed out.<|reference_end|>
@article{majumdar2002exact,
    title={Exact Solution of a Drop-push Model for Percolation},
    author={Satya N. Majumdar and David S. Dean},
    journal={Phys. Rev. Lett., 89, 115701 (2002)},
    year={2002},
    doi={10.1103/PhysRevLett.89.115701},
    archivePrefix={arXiv},
    eprint={cond-mat/0205336},
    primaryClass={cond-mat.stat-mech cs.DS math.PR}
}