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 those of the ordinary percolation. The relevance of our results to computer science is pointed out.