We prove existence of the large deviation principle, with a proper convex rate function, for the distribution of the renormalized distance from the origin of a random walk on a free product of finitely generated groups. As a consequence, we derive the same principle for nearest-neighbour random walks on regular trees.
This work owes a major debt to Çagri Sert, to whom the author expresses his gratitude for several insightful comments and enlightening conversations. Special thanks go to the referee for a thorough reading of the article, which tremendously helped improve its quality. Lastly, we would like to thank Manfred Einsiedler for valuable remarks on a preliminary version, as well as Sebastian Müller for providing many useful references and observations.
Emilio Corso. "Large deviations for random walks on free products of finitely generated groups." Electron. J. Probab. 26 1 - 22, 2021. https://doi.org/10.1214/21-EJP695