Potential Analysis

, Volume 50, Issue 4, pp 541–564 | Cite as

Upper Escape Rate for Weighted Graphs via Metric Graphs

  • Xueping HuangEmail author
  • Liang Niu


The upper escape rate for a Markov process is a natural partial generalization of the celebrated Khintchine’s law of the iterated logarithm. In this article, we present a new proof of the sharp volume growth criterion for upper escape rate of continuous time random walks on weighted graphs in Huang and Shiozawa (Stoch. Process Appl. 124(1), 317–347 2014). Our proof is based on comparison with a corresponding modified metric graph, and this technique allows us to remove the restriction on vertex weight in Huang and Shiozawa (Stoch. Process Appl. 124(1), 317–347 2014) as well.


Escape rate Upper rate function Continuous time random walks Markov chains Weighted graphs Metric graphs 

Mathematics Subject Classification (2010)

Primary 60J27; Secondary 05C81 


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The authors gratefully acknowledge financial support from National Natural Science Foundation of China(Grant No. 11601238), and The Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology(Grant No. 2015r053). X. H. was also partially supported by the SMART project of GSIS, Tohoku University.

We thank the anonymous referee for carefully reading the article and helping us improve the presentation.


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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNanjing University of Information Science and TechnologyNanjingChina

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