Largest Component and Sharpness in Subcritical Continuum Percolation

2024/07/15 by Küpper, Niclas, Penrose, Mathew D. · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.10715

Abstract

We investigate the behavior of large connected components in the Random Connection Model in the subcritical regime with any bounded connection function. We show that the asymptotic size of the largest component restricted to a window is the log of the volume of that window. We adopt methods from the discrete setting, including a sharpness result.

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• On strong sharp phase transition in the random connection model
• Exponential decay for the random connection model using asymptotic transitivity

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