Let G be an infinite connected graph with vertex set V. Let be the simple random walk on G and let be a collection of i.i.d. random variables which are independent of the random walk. Define the random walk in random scenery as , and the normalization variables and . For and , the d-ary tree, we provide large deviations results for the self-normalized process under only finite moment assumptions on the scenery.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 692452).
I would like to thank my M.Sc. advisor Ofer Zeitouni for his guidance and support throughout all stages of this work. Thank you to both reviewers for providing detailed feedback that greatly improved the content and flow of the manuscript.
"Moderate deviations for the self-normalized random walk in random scenery." Electron. J. Probab. 26 1 - 16, 2021. https://doi.org/10.1214/21-EJP607