Strong Law of Large Numbers for a Function of the Local Time of a Transient Random Walk on a Group

Yinshan Chang (), Qinwei Chen (), Qian Meng () and Xue Peng ()
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Yinshan Chang: Sichuan University
Qinwei Chen: Sichuan University
Qian Meng: University of Washington
Xue Peng: Sichuan University

Journal of Theoretical Probability, 2026, vol. 39, issue 1, 1-16

Abstract: Abstract This paper presents the strong law of large numbers for a function of the local time of a transient random walk on a group, extending the research of Asymont and Korshunov (J Theoret Probab 33(4):2315–2336, 2020. https://doi.org/10.1007/s10959-019-00937-6 ) for random walks on the integer lattice $$\mathbb {Z}^{d}$$ Z d . Under some weaker conditions, we prove that a certain function of the local times converges almost surely and in $$L^{1}$$ L 1 and $$L^{2}$$ L 2 . The proof is based mainly on the subadditive ergodic theorem.

Keywords: Transient random walk on a group; Local time; Strong law of large numbers; 60G50; 60J55; 60F15 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10959-025-01464-3

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