2018/02/06 by Giovanni Luca Torrisi, Torrisi, Giovanni Luca, Michele Garetto +3
Computer Science · Mathematics · Physics and Astronomy · #05C80 #60F10 #60K35 #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Opinion Dynamics and Social Influence #Performance (cs.PF) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cs.PF #math.PR #msc:05C80 #msc:60F10 #msc:60K35
paper · pdf · doi:10.48550/arxiv.1802.01847
44 pages
openalex publication_date 2018/02/06 · arxiv created 2020/01/16 · arxiv updated 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Erdös--Rényi random graph Gn,p and we analyze the simple irreversible epidemic process on the graph, known in the literature as bootstrap percolation. We give a quantitative version of some results by Janson et al. (2012), providing a fine asymptotic analysis of the final size An^* of active nodes, under a suitable super-critical regime. More specifically, we establish large deviation principles for the sequence of random variables \(n- An^*)/(f(n))\n≥ 1 with explicit rate functions and allowing the scaling function f to vary in the widest possible range.