Abstract
In this article we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Our methods rely on local central limit theorems for convergence of random walks on discretizations of smooth domains to Reflected Brownian motion.
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Ganguly, S., Peres, Y. Convergence of Discrete Green Functions with Neumann Boundary Conditions. Potential Anal 46, 799–818 (2017). https://doi.org/10.1007/s11118-016-9602-x
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DOI: https://doi.org/10.1007/s11118-016-9602-x