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The access time of random walks on trees with given partition

Author

Listed:
  • Feng, Lihua
  • Liu, Weijun
  • Lu, Lu
  • Wang, Wei
  • Yu, Guihai

Abstract

Denote by T(s,t) the set of trees, whose vertex set can be partitioned into two independent sets of sizes s and t respectively. Given a tree T with stationary distribution π and a vertex v∈T, the access time HT(π,v) is the expected length of optimal stopping rules from π to v. In this paper, we get a sharp upper bound for maxv∈THT(π,v) and a sharp lower bound for minv∈THT(π,v) among T(s,t), respectively. The corresponding extremal graphs are also obtained. As a byproduct, it is proved that the path Pn maximizes maxv∈THT(π,v) and the star K1,n−1 minimizes minv∈THT(π,v) among all trees on n vertices.

Suggested Citation

  • Feng, Lihua & Liu, Weijun & Lu, Lu & Wang, Wei & Yu, Guihai, 2022. "The access time of random walks on trees with given partition," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    • Handle: RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002478
    DOI: 10.1016/j.amc.2022.127173
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    References listed on IDEAS

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    1. Göbel, F. & Jagers, A. A., 1974. "Random walks on graphs," Stochastic Processes and their Applications, Elsevier, vol. 2(4), pages 311-336, October.
    2. Palacios, José Luis, 2009. "On hitting times of random walks on trees," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 234-236, January.
    3. José Luis Palacios, 2009. "On the Moments of Hitting Times for Random Walks on Trees," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-4, October.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Tree; Random walk; Stopping rule;
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