A Hitting Time Formula for the Discrete Green's Function
Published in Combinatorics, Probability and Computing, 2016
A. Beveridge, A Hitting Time Formula for the Discrete Green's Function, Combinatorics, Probability and Computing, Vol. 25, (2016) pp. 362-379.
Preprint link: https://arxiv.org/abs/1505.06989
The discrete Green's function (without boundary) is a pseudo-inverse of the combinatorial Laplace operator of a graph. We reveal the intimate connection between Green's function and the theory of exact stopping rules for random walks on graphs. We give an elementary formula for Green's function in terms of state-to-state hitting times of the underlying graph.