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A large deviation approach to super-critical bootstrap percolation on the random graph Gn,p

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  • Torrisi, Giovanni Luca
  • Garetto, Michele
  • Leonardi, Emilio

Abstract

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.

Suggested Citation

  • Torrisi, Giovanni Luca & Garetto, Michele & Leonardi, Emilio, 2019. "A large deviation approach to super-critical bootstrap percolation on the random graph Gn,p," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1873-1902.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:6:p:1873-1902
    DOI: 10.1016/j.spa.2018.06.006
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