Balls and Bins -- Simple Concentration Bounds

Ernst Schulte-Geers; Bo Waggoner

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arXiv · 2205.14494

Balls and Bins -- Simple Concentration Bounds

Ernst Schulte-Geers·Bo Waggoner

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Abstract

Concentration bounds are given for throwing balls into bins independently according to a distribution $p$. The probability of a $k$-loaded bin after $m$ balls is shown to be controlled on both sides by $\rho_{m,k} := m \|p\|_k / k$. This gives concentration inequalities for the maximum load as well as for the waiting time until a $k$-loaded bin.

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Ernst Schulte-Geers, Bo Waggoner. 2022-05-28. Balls and Bins -- Simple Concentration Bounds. https://arxiv.org/abs/2205.14494

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