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Local probabilities of randomly stopped sums of power law lattice random variables
Mindaugas Bloznelis · 2018-01-03 · via math.PR updates on arXiv.org

Let $X_1$ and $N\ge 0$ be integer valued power law random variables. For a randomly stopped sum $S_N=X_1+\cdots+X_N$ of independent and identically distributed copies of $X_1$ we establish a first order asymptotics of the local probabilities $P(S_N=t)$ as $t\to+\infty$. Using this result we show the $k^{-δ}$, $0\le δ\le 1$ scaling of the local clustering coefficient (of a randomly selected vertex of degree $k$) in a power law affiliation network.

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