Limit Theorems for Random Sums of Random Summands

David Grzybowski

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arXiv · 2010.00483

Limit Theorems for Random Sums of Random Summands

David Grzybowski

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Abstract

We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy tails. We also prove a version of Hoeffding's combinatorial central limit theorem and results for summands taken uniformly from a random sample. These results are proved with concentration of measure techniques.

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David Grzybowski. 2020-10-01. Limit Theorems for Random Sums of Random Summands. https://arxiv.org/abs/2010.00483

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