Co-author: Jason Miller (MIT)
Let X be a simple random walk in Zdn and let tcov be the expected amount of time it takes for X to visit all of the vertices of Zdn. For α∈(0,1), the set Lα of α-late points consists of those x∈Zdn which are visited for the first time by X after time αtcov. Oliveira and Prata (2011) showed that the distribution of L1 is close in total variation to a uniformly random set. The value α=1 is special, because |L1| is of order 1 uniformly in n, while for α
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