A note on the random constrained-degree percolation model on \mathbbL²

2026/07/28 by Marco Ticse
#math.PR #math-ph #math.MP

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Abstract

This note considers a constrained-degree percolation model in a random environment on the square lattice, where each vertex is assigned a random degree constraint, and edges attempt to open at random times. We prove that whenever an infinite open cluster exists, it is almost surely unique, implying the positivity of the connectivity function in the supercritical regime.

Citations

• Constrained-degree percolation on the hypercubic lattice: uniqueness and some of its consequences
• A strong FKG inequality for multiple events
• Constrained-degree percolation in random environment
• The Constrained-degree percolation model
• Constrained percolation in two dimensions
• Percolation on interacting networks with feedback-dependency links
• Random graphs with forbidden vertex degrees

Related

• Constrained-degree percolation in random environment
• The Constrained-degree percolation model
• Constrained-degree percolation on the hypercubic lattice: uniqueness and some of its consequences
• Sharpness of the phase transition for constrained-degree percolation
• Quenched invariance principle for simple random walk on clusters in\n correlated percolation models