Edge- and vertex-reinforced random walks with super-linear reinforcement on infinite graphs

@article{Cotar2015EdgeAV,
  title={Edge- and vertex-reinforced random walks with super-linear reinforcement on infinite graphs},
  author={Codina Cotar and Debleena Thacker},
  journal={arXiv: Probability},
  year={2015}
}
In this paper we introduce a new simple but powerful general technique for the study of edge- and vertex-reinforced processes with super-linear reinforcement, based on the use of order statistics for the number of edge, respectively of vertex, traversals. The technique relies on upper bound estimates for the number of edge traversals, proved in a different context by Cotar and Limic [Ann. Appl. Probab. (2009)] for finite graphs with edge reinforcement. We apply our new method both to edge- and… 

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