The shape of large balls in highly supercritical percolation

2013/05/01 by Basdevant, Anne-Laure, Nathanaël Enriquez, Lucas Gerin +3
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Random Matrices and Applications

paper · doi:10.48550/arxiv.1305.0104

Abstract

We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on ℤ. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.

Related

• Distances in the highly supercritical percolation cluster
• Large deviations of the giant in supercritical kernel-based spatial random graphs
• Supercritical loop percolation on ℤ^d for d≥ 3
• Continuity of the critical value and a shape theorem for long-range percolation
• Large deviations for simple random walk on percolations with long-range correlations