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- W2556724100 abstract "Let ${B_k}_{k=1}^infty, {X_k}_{k=1}^infty$ all be independent random variables. Assume that ${B_k}_{k=1}^infty$ are ${0,1}$-valued Bernoulli random variables satisfying $B_kstackrel{text{dist}}{=}text{Ber}(p_k)$, with $sum_{k=1}^infty p_k=infty$, and assume that ${X_k}_{k=1}^infty$ satisfy: $X_k>0, mu_kequiv EX_k 0$ and let $$ begin{aligned} &mu_nsim c_mu n^{a_0}prod_{j=1}^{J_mu}(log^{(j)}n)^{a_j}, p i &iii. a_j=0, 0le jle J_p-1, text{and} a_{J_p}>0, end{aligned} $$ then $ lim_{ntoinfty}W_nstackrel{text{dist}}{=}frac1{theta}text{GD}(theta), text{where} theta=frac{c_p}{a_{J_p}}. $ Otherwise, $lim_{ntoinfty}W_nstackrel{text{dist}}{=}c$, for some $cin[0,1]$. We also give an application to the statistics of the number of inversions in certain shuffling schemes." @default.
- W2556724100 created "2016-11-30" @default.
- W2556724100 creator A5032276033 @default.
- W2556724100 date "2016-11-22" @default.
- W2556724100 modified "2023-09-27" @default.
- W2556724100 title "On the strange domain of attraction to generalized Dickman distributions for sums of independent random variables" @default.
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