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Spatial preferential attachment models: robustness revisited
Abstract
We investigate robustness under percolation in the degree-driven spatial preferential attachment model. Consider a profile that is regularly varying with exponent −δ, where δ>1, and an attachment rule with asymptotic slope γ∈(0,1). Jacob and Mörters (Ann. Probab. 45 (2017)) proved robustness when δ(1/γ−1)<1. We prove the converse in the strict regime: if δ(1/γ−1)>1, then sufficiently strong Bernoulli vertex thinning destroys the giant component. In particular, the strict robustness boundary coincides with that of the age-dependent random connection model.
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BibTeX
@misc{gracar2026spatial,
title = {{Spatial preferential attachment models: robustness revisited}},
author = {Peter Gracar and Christian Mönch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29853},
eprint = {2610.29853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29853},
}
RIS
TY - UNPB
TI - Spatial preferential attachment models: robustness revisited
AU - Peter Gracar
AU - Christian Mönch
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29853
UR - https://arxiv.org/abs/2610.29853
AB - We investigate robustness under percolation in the degree-driven spatial preferential attachment model. Consider a profile that is regularly varying with exponent −δ, where δ>1, and an attachment rule with asymptotic slope γ∈(0,1). Jacob and Mörters (Ann. Probab. 45 (2017)) proved robustness when δ(1/γ−1)<1. We prove the converse in the strict regime: if δ(1/γ−1)>1, then sufficiently strong Bernoulli vertex thinning destroys the giant component. In particular, the strict robustness boundary coincides with that of the age-dependent random connection model.
ER -