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math.PR2026
How Robust is Scale-Free Structure? Phase Transitions in Preferential Attachment Model under Attack?
Xiaoyun Gong, Gennady Samorodnitsky
Will an attack on a network affect its structure in a major way? In this work we study this question by investigating a dynamic preferential attachment-type graph in which an attac…
math.PR2025
Interlacing sequences resulting from an interval split-merge dynamics and the induced probability measures
Serge Cohen, James Norris, Michel Pain +1
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting i…
math.PR2024
Degree counts in random simplicial complexes of the preferential attachment type
Takashi Owada, Gennady Samorodnitsky
We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing -simplices with prob…