Discrete Green's functions and random walks on graphs

@article{Xu2013DiscreteGF,
  title={Discrete Green's functions and random walks on graphs},
  author={Hao Xu and Shing-Tung Yau},
  journal={J. Comb. Theory, Ser. A},
  year={2013},
  volume={120},
  pages={483-499}
}
We prove an explicit formula of Chung-Yau@?s Discrete Green@?s functions as well as hitting times of random walks on graphs. The formula is expressed in terms of two natural counting invariants of graphs. Uniform derivations of Green@?s functions and hitting times for trees and other special graphs are given. 

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