• Corpus ID: 209515446

Clustering and percolation on superpositions of Bernoulli random graphs

@article{Bloznelis2019ClusteringAP,
  title={Clustering and percolation on superpositions of Bernoulli random graphs},
  author={Mindaugas Bloznelis and Lasse Leskela},
  journal={arXiv: Probability},
  year={2019}
}
Let $W=\{w_1,\dots, w_m\}$ be a finite set. Given integers $x_1,\dots,x_n\in[0, m]$ and numbers $q_1,...,q_n \in [0,1]$, let $D_1,\dots,D_n$ be independent uniformly distributed random subsets of $W$ of sizes $|D_i|=x_i$, $1\le i\le n$. Let $G_n$ be the union of independent Bernoulli random graphs $G(x_i, q_i),$ $1\le i\le n$, with vertex sets $D_1,\dots, D_n$. For $m,n\to+\infty$ such that $m=\Theta(n)$ we show that $G_n$ admits a tunable (asymptotic) power law degree distribution and non… 
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