For any subcritical random connection model with integrable connection function, the cluster size distribution has an exponential tail.
Largest component and sharpness in continuum percolation
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We investigate the behavior of large connected components in the Poisson Random Connection model in non-critical regimes with any bounded connection function. We show that the asymptotic size of the largest component restricted to a window grows logarithmically in the volume of that window in the subcritical case, and linearly in the supercritical case. We also prove a sharpness result saying that the order of the cluster at the origin has an exponentially decaying tail in the subcritical regime.
citation-role summary
background 1
citation-polarity summary
fields
math.PR 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Exponential decay for the random connection model using asymptotic transitivity
For any subcritical random connection model with integrable connection function, the cluster size distribution has an exponential tail.