A note on the random constrained-degree percolation model on $\mathbb{L}^2$

Marco Ticse

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arXiv · 2607.25277

A note on the random constrained-degree percolation model on $\mathbb{L}^2$

Marco Ticse

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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.

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Marco Ticse. 2026-07-28. A note on the random constrained-degree percolation model on $\mathbb{L}^2$. https://arxiv.org/abs/2607.25277

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