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PreprintCC BY 4.0arXiv

Cascade Surviving Cores via Local Limits

  • Souvik Dhara
  • Manish Pandey
  • Leonard J. Schulman
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Abstract

We consider a general class of cascading processes on marked networks, in which vertices are iteratively deleted according to a local vertex property. Under marked local-weak convergence, we establish a necessary and sufficient condition for the proportion of vertices in the final stable set to converge to the survival probability in the limiting network. Under this condition, we also obtain convergence of the proportions of vertices in subsets specified by local properties.

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Cite

BibTeXRIS
BibTeX
@misc{dhara2026cascade,
  title = {{Cascade Surviving Cores via Local Limits}},
  author = {Souvik Dhara and Manish Pandey and Leonard J. Schulman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16242},
  eprint = {2609.16242},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16242},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Cascade Surviving Cores via Local Limits
AU  - Souvik Dhara
AU  - Manish Pandey
AU  - Leonard J. Schulman
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16242
UR  - https://arxiv.org/abs/2609.16242
AB  - We consider a general class of cascading processes on marked networks, in which vertices are iteratively deleted according to a local vertex property. Under marked local-weak convergence, we establish a necessary and sufficient condition for the proportion of vertices in the final stable set to converge to the survival probability in the limiting network. Under this condition, we also obtain convergence of the proportions of vertices in subsets specified by local properties.
ER  -