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Consider an expander graph in which a $\mu$ fraction of the vertices aremarked. A random walk starts at a uniform vertex and at each step continues toa random neighbor. Gillman showed in 1993 that the number of marked verticesseen in a random walk of length $n$ is concentrated around its expectation,$\Phi := \mu n$, independent of the size of the graph. Here we provide a newand sharp tail bound, improving on the existing bounds whenever $\mu$ is nottoo large.

A Sharp Tail Bound for the Expander Random Sampler