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- W4300814458 abstract "For the critical Galton--Watson process with geometric offspring distributions we provide sharp barrier estimates for barriers which are (small) perturbations of linear barriers. These are useful in analyzing the cover time of finite graphs in the critical regime by random walk, and the Brownian cover times of compact two dimensional manifolds. As an application of the barrier estimates, we prove that if $C_L$ denotes the cover time of the binary tree of depth $L$ by simple walk, then $sqrt{C_L/2^{L+1}} -sqrt{2log 2} L+log L/sqrt{2log 2}$ is tight. The latter improves results of Aldous (1991), Bramson and Zeitouni (2009) and Ding and Zeitouni (2012). In a subsequent article we use these barrier estimates to prove tightness of the Brownian cover time for the two-dimensional sphere." @default.
- W4300814458 created "2022-10-04" @default.
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- W4300814458 date "2017-02-10" @default.
- W4300814458 modified "2023-09-27" @default.
- W4300814458 title "Barrier estimates for a critical Galton--Watson process and the cover time of the binary tree" @default.
- W4300814458 doi "https://doi.org/10.48550/arxiv.1702.03189" @default.
- W4300814458 hasPublicationYear "2017" @default.
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