NDLI: The Best Mixing Time for Random Walks on Trees

Content Provider	Springer Nature Link
Author	Beveridge, Andrew Youngblood, Jeanmarie
Copyright Year	2016
Abstract	We characterize the extremal structures for mixing walks on trees that start from the most advantageous vertex. Let $$G=(V,E)$$ be a tree with stationary distribution $$\pi $$ . For a vertex $$v \in V$$ , let $$H(v,\pi )$$ denote the expected length of an optimal stopping rule from v to $$\pi $$ . The best mixing time for G is $$\min _{v \in V} H(v,\pi )$$ . We show that among all trees with $$\|V\|=n$$ , the best mixing time is minimized uniquely by the star. For even n, the best mixing time is maximized by the uniquely path. Surprising, for odd n, the best mixing time is maximized uniquely by a path of length $$n-1$$ with a single leaf adjacent to one central vertex.
Starting Page	2211
Ending Page	2239
Page Count	29
File Format	PDF
ISSN	09110119
Journal	Graphs and Combinatorics
Volume Number	32
Issue Number	6
e-ISSN	14355914
Language	English
Publisher	Springer Japan
Publisher Date	2016-05-21
Publisher Place	Tokyo
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Tree Markov chain Random walk Stopping rule Mixing time Combinatorics Engineering Design
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science

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The Best Mixing Time for Random Walks on Trees