Perturbing the Shortest Path on a Critical Directed Square Lattice

Abstract

We investigate the behaviour of the shortest path on a directed two-dimensional square lattice for bond percolation at the critical probability $p_c$ . We observe that flipping an edge lying on the shortest path has a non-local effect in the form of power-law distributions for both the differences in shortest path lengths and for the minimal enclosed areas. Using maximum likelihood estimation and extrapolation we find the exponents $\alpha =1.36\pm 0.01$ for the path length differences and $\beta =1.186\pm 0.001$ for the enclosed areas.

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Cited by in corpus (2)

• From one-way streets to percolation on random mixed graphs
• Sequential disruption of the shortest path in critical percolation