Open Access
2021 Large deviations for random walks on free products of finitely generated groups
Emilio Corso
Author Affiliations +
Electron. J. Probab. 26: 1-22 (2021). DOI: 10.1214/21-EJP695


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.


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Emilio Corso. "Large deviations for random walks on free products of finitely generated groups." Electron. J. Probab. 26 1 - 22, 2021.


Received: 16 April 2020; Accepted: 27 August 2021; Published: 2021
First available in Project Euclid: 25 November 2021

Digital Object Identifier: 10.1214/21-EJP695

Primary: 05C81 , 60B15 , 60F10 , 60G50

Keywords: cone types , ‎free groups , Free Products , Gromov-hyperbolic groups , large deviations , Random walks , regular trees

Vol.26 • 2021
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