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

Local probabilities of randomly stopped sums of power law lattice random variables