Tail estimates for sums of variables sampled from a random walk
Abstract
We prove tail estimates for variables , where 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 , 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.
Cite
@article{arxiv.math/0608740,
title = {Tail estimates for sums of variables sampled from a random walk},
author = {Roy Wagner},
journal= {arXiv preprint arXiv:math/0608740},
year = {2007}
}
Comments
V4: published version; theorems 1&2 slightly revised V3: Improved Bennett inequality V2: Corrected version. Confusion concerning definition of $\beta$ resolved. Results given both in terms of sepctral gap and second largest absolute value of an eigenvalue. Sign error in statement of Theorem 4 corrected. Other minor and cosmetic corrections included as well