Timeline for Does the Green's function of the simple random walk on $\mathbb Z^d$ always vary locally?

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Feb 17, 2021 at 2:12	comment	added	fedja		@IosifPinelis It is pretty clear that the symmetric random walk was meant, but, indeed, you raise an interesting question if the Green function can be locally constant for other finitely supported assignments of probabilities (let's assume that we deal with non-degenerate case when every point is reachable and we don't care about the possibility of finitely many exceptions to eliminate some trivial counterexamples).
Feb 17, 2021 at 1:40	comment	added	Iosif Pinelis		@NateEldredge : I think you meant $2d$ rather than $2^d$. As for what the OP meant exactly by the "simple random walk", I was not sure. Therefore, because symmetry was not mentioned by the OP, I followed en.wikipedia.org/wiki/Random_walk: "In a simple random walk, the location can only jump to neighboring sites of the lattice, forming a lattice path. In simple symmetric random walk on a locally finite lattice, the probabilities of the location jumping to each one of its immediate neighbors are the same."
Feb 17, 2021 at 0:10	comment	added	Nate Eldredge		I assumed that "simple random walk on $\mathbb{Z}^d$" means the one whose transitions are selected uniformly from the $2^d$ edges of each vertex.
Feb 16, 2021 at 23:13	history	answered	Iosif Pinelis	CC BY-SA 4.0