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- W4289699956 abstract "We study tree-indexed random walks as introduced by Benjamini, Haggstrom, and Mossel, i.e. labelings of a tree for which adjacent vertices have labels differing by 1. It is a conjecture of those authors that the distribution of the range for any such tree is dominated by that of a path on the same number of edges. The two main variants of this conjecture considered in the literature are the $textit{standard}$ walks, in which adjacent vertices must have labels differing by $textit{exactly}$ 1, and $textit{lazy}$ walks, in which adjacent vertices must have labels differing by $textit{at most}$ 1. We confirm this conjecture for all trees in the lazy case and provide some partial results in the standard case." @default.
- W4289699956 created "2022-08-04" @default.
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- W4289699956 date "2018-08-13" @default.
- W4289699956 modified "2023-10-16" @default.
- W4289699956 title "On the Distribution of Range for Tree-Indexed Random Walks" @default.
- W4289699956 doi "https://doi.org/10.48550/arxiv.1808.04261" @default.
- W4289699956 hasPublicationYear "2018" @default.
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