Tail estimates for sums of variables sampled from a random walk

Details Tail estimates for sums of variables sampled from a random walk Tail estimates for sums of variables sampled from a random walk

2006-08-30

arxiv.org/abs/math/0608740v4

Mathematics

Probability

V4: published version; theorems 1&2 slightly revised V3: Improved Bennett inequality V2: Corrected version. Confusion concerni

Scientific paper

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$, its variance, and the spectrum of the graph. Our proofs are more elementary than other proofs in the literature, and our results are sharper. We obtain Bernstein and Bennett-type inequalities, as well as an inequality for subgaussian variables.

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