Abstract
The right kind of connectivity turns out to be both necessary and sufficient for large scale cascades to propagate in a network. After outlining percolation theory on random graphs, we develop an idea known as “bootstrap percolation” that proves to be the precise concept needed for unravelling and understanding the growth of simple network cascades. These principles are illustrated by the famous Watts model of information cascades.
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- 1.
For any \(0\le k\le N\) and \(p\in [0,1]\), the Binomial probability \(\mathrm{Bin}(N, p,k)=\left( {\begin{array}{c}N\\ k\end{array}}\right) p^k(1-p)^{N-k}\) is the probability of exactly k successes in N independent Bernoulli trials each with success probability p.
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Hurd, T.R. (2016). Percolation and Cascades. In: Contagion! Systemic Risk in Financial Networks. SpringerBriefs in Quantitative Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-33930-6_4
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DOI: https://doi.org/10.1007/978-3-319-33930-6_4
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Online ISBN: 978-3-319-33930-6
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