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Laws of the iterated and single logarithm for sums of independent indicators, with applications to the Ginibre point process and Karlin’s occupancy scheme

Author

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  • Buraczewski, Dariusz
  • Iksanov, Alexander
  • Kotelnikova, Valeriya

Abstract

We prove a law of the iterated logarithm (LIL) for an infinite sum of independent indicators parameterized by t and monotone in t as t→∞. It is shown that if the expectation b and the variance a of the sum are comparable, then the normalization in the LIL includes the iterated logarithm of a. If the expectation grows faster than the variance, while the ratio logb/loga remains bounded, then the normalization in the LIL includes the single logarithm of a (so that the LIL becomes a law of the single logarithm). Applications of our result are given to the number of points of the infinite Ginibre point process in a disk and the number of occupied boxes and related quantities in Karlin’s occupancy scheme.

Suggested Citation

  • Buraczewski, Dariusz & Iksanov, Alexander & Kotelnikova, Valeriya, 2025. "Laws of the iterated and single logarithm for sums of independent indicators, with applications to the Ginibre point process and Karlin’s occupancy scheme," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:spapps:v:183:y:2025:i:c:s0304414925000389
    DOI: 10.1016/j.spa.2025.104597
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