Abstract
We find uniform lower bounds on the drift for a large family of random walks on graph products, of the form for . This includes the simple random walk for a right-angled Artin group with a sparse defining graph. This is done by extending an argument of Gouëzel, along with the combinatorial notion of a piling introduced by Crisp, Godelle, and Wiest. We do not use any moment conditions, instead considering random walks which alternate between one measure uniformly distributed on vertex groups, and another measure over which we make no assumptions.
Acknowledgments
The author would like to thank Giulio Tiozzo for many helpful conversations and comments. The author would also like to thank the referees for multiple helpful comments which greatly improved the exposition, and for pointing out helpful references. This work was completed under funding from an NSERC USRA.
Citation
Kunal Chawla. "Effective drift estimates for random walks on graph products." Electron. Commun. Probab. 28 1 - 12, 2023. https://doi.org/10.1214/23-ECP546
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