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Exact Solution of a Drop-push Model for Percolation

Satya N. Majumdar·David S. Dean
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Abstract

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.

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Satya N. Majumdar, David S. Dean. 2002-05-16. Exact Solution of a Drop-push Model for Percolation. https://doi.org/10.1103/physrevlett.89.115701

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