A law of the iterated logarithm for small counts in Karlin’s occupancy scheme
Alexander Iksanov,
Valeriya Kotelnikova
Abstract:In the Karlin infinite occupancy scheme, balls are thrown independently into an infinite array of boxes $1,2,\dots $ , with probability ${p_{k}}$ of hitting the box k. For $j,n\in \mathbb{N}$, denote by ${\mathcal{K}_{j}^{\ast }}(n)$ the number of boxes containing exactly j balls provided that n balls have been thrown. Small counts are the variables ${\mathcal{K}_{j}^{\ast }}(n)$, with j fixed. The main result is a law of the iterated logarithm (LIL) for the small counts as the number of balls thrown becomes l… Show more
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