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- W2952334863 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2015 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Surprise probabilities in Markov chainsJames Norris, Yuval Peres, and Alex ZhaiJames Norris, Yuval Peres, and Alex Zhaipp.1759 - 1773Chapter DOI:https://doi.org/10.1137/1.9781611973730.118PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract In a Markov chain started at a state x, the hitting time τ(y) is the first time that the chain reaches another state y. We study the probability Px(τ(y) = t) that the first visit to y occurs precisely at a given time t. Informally speaking, the event that a new state is visited at a large time t may be considered a “surprise”. We prove the following three bounds: In any Markov chain with n states, In a reversible chain with n states, For random walk on a simple graph with n ≥ 2 vertices, We construct examples showing that these bounds are close to optimal. The main feature of our bounds is that they require very little knowledge of the structure of the Markov chain. To prove the bound for random walk on graphs, we establish the following estimate conjectured by Aldous, Ding and Oveis-Gharan (private communication): For random walk on an n-vertex graph, for every initial vertex x, Previous chapter Next chapter RelatedDetails Published:2015ISBN:978-1-61197-374-7eISBN:978-1-61197-373-0 https://doi.org/10.1137/1.9781611973730Book Series Name:ProceedingsBook Code:PRDA15Book Pages:viii + 2048" @default.
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- W2952334863 date "2014-12-22" @default.
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- W2952334863 title "Surprise probabilities in Markov chains" @default.
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