Yin-Feng Zhu

Paths maximize the expected range of graph-indexed random walks

We prove that a path maximizes the expected range of a uniformly chosen graph homomorphism into the integers, with one vertex pinned at zero, among all connected bipartite graphs of the same order. This establishes the expectation form of the Benjamini--H\"aggstr\"om--Mossel conjecture. The proof restricts and rescales...