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On partial sums of hitting times

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  • Palacios, José Luis
  • Renom, José M.

Abstract

We conjecture that if Tj is the hitting time of vertex j then ∑jEiTj≥(N−1)2, for all i, for a random walk on any connected graph G=(V,E) with |E|=N. We prove the conjecture for a family of graphs containing the regular graphs and obtain slightly better bounds for trees and non-regular edge-transitive graphs.

Suggested Citation

  • Palacios, José Luis & Renom, José M., 2012. "On partial sums of hitting times," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 783-785.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:783-785
    DOI: 10.1016/j.spl.2011.12.012
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    References listed on IDEAS

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    1. Bapat, R.B., 2011. "On the first passage time of a simple random walk on a tree," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1552-1558, October.
    2. Palacios, JoséLuis & Renom, JoséMiguel, 1998. "Random walks on edge transitive graphs," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 29-34, January.
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    Cited by:

    1. Yoon, Hyungkuk & Kim, Bara & Kim, Jeongsim, 2020. "Lower bounds on partial sums of expected hitting times," Statistics & Probability Letters, Elsevier, vol. 160(C).

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    More about this item

    Keywords

    Effective resistance; Kirchhoff index;

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