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math.PR2026
Cascade Surviving Cores via Local Limits
Souvik Dhara, Manish Pandey, Leonard J. Schulman
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 conve…
math.PR2026
Waning Immunity Fails to Restore a Positive Epidemic Threshold on Power-Law Networks
Zihao He, Souvik Dhara, Debankur Mukherjee
In a seminal work, Chatterjee and Durrett (2009) established that for the SIS epidemic process on random graphs with power-law degree distributions, the infection survives for an e…