In this paper, we consider the linearly reinforced and the once-reinforced random walk models in the transient phase on trees. We show the large deviations for the upper tails for both models. We also show the exponential decay for the lower tail in the once-reinforced random walk model. However, the lower tail is in polynomial decay for the linearly reinforced random walk model.
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The author would like to thank a careful referee for his many valuable comments, which corrected a few mistakes and improved the quality of this paper. He would also like to thank Takei M. for pointing out a few typos and a few references.
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Zhang, Y. Large deviations in the reinforced random walk model on trees. Probab. Theory Relat. Fields 160, 655–678 (2014). https://doi.org/10.1007/s00440-013-0537-5
- Reinforced random walks on trees
- Large deviation
Mathematics Subject Classification