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A Central Limit Theorem for the Mean Starting Hitting Time for a Random Walk on a Random Graph

Author

Listed:
  • Matthias Löwe

    (Universität Münster)

  • Sara Terveer

    (Universität Münster)

Abstract

We consider simple random walk on a realization of an Erdős–Rényi graph with n vertices and edge probability $$p_n$$ p n . We assume that $$n p^2_n/(\log \mathrm{n})^{16 \xi } \rightarrow \infty $$ n p n 2 / ( log n ) 16 ξ → ∞ for some $$\xi >1$$ ξ > 1 defined below. This in particular implies that the graph is asymptotically almost surely (a.a.s.) connected. We show a central limit theorem for the average starting hitting time, i.e., the expected time it takes the random walker on average to first hit a vertex j when starting in a fixed vertex i. The average is taken with respect to $$\pi _j$$ π j , the invariant measure of the random walk.

Suggested Citation

  • Matthias Löwe & Sara Terveer, 2023. "A Central Limit Theorem for the Mean Starting Hitting Time for a Random Walk on a Random Graph," Journal of Theoretical Probability, Springer, vol. 36(2), pages 779-810, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01195-9
    DOI: 10.1007/s10959-022-01195-9
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    References listed on IDEAS

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    1. Helali, Amine & Löwe, Matthias, 2019. "Hitting times, commute times, and cover times for random walks on random hypergraphs," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
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