A Sharp Tail Bound for the Expander Random Sampler

Shravas Rao; Oded Regev

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arXiv · 1703.10205

A Sharp Tail Bound for the Expander Random Sampler

Shravas Rao·Oded Regev

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Abstract

Consider an expander graph in which a $μ$ fraction of the vertices are marked. A random walk starts at a uniform vertex and at each step continues to a random neighbor. Gillman showed in 1993 that the number of marked vertices seen in a random walk of length $n$ is concentrated around its expectation, $Φ:= μn$, independent of the size of the graph. Here we provide a new and sharp tail bound, improving on the existing bounds whenever $μ$ is not too large.

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Shravas Rao, Oded Regev. 2017-08-23. A Sharp Tail Bound for the Expander Random Sampler. https://arxiv.org/abs/1703.10205

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