Exact Solution of a Drop-push Model for Percolation

TL;DR

This paper introduces an exact solution for a one-dimensional drop-push percolation model inspired by hashing algorithms, revealing unique spatial correlations and critical exponents distinct from ordinary percolation.

Contribution

It provides the first exact analytical solution for the drop-push percolation model, highlighting its nontrivial correlations and differing critical behavior from standard models.

Findings

The model exhibits nontrivial spatial correlations due to its dynamics.

Critical exponents differ from those of ordinary percolation.

Results have implications for computer science algorithms.

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.