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Fluctuations of the giant of Poisson random graphs

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  • Clancy, David

Abstract

Enriquez et al. (2025) have established process-level fluctuations for the giant of the dynamic Erdős–Rényi random graph above criticality and show that the limit is a centered Gaussian process with continuous sample paths. A random walk proof was recently obtained by Corujo et al. (2024). We show that a similar result holds for rank-one inhomogeneous models whenever the empirical weight distribution converges to a limit and its second moment converges as well.

Suggested Citation

  • Clancy, David, 2026. "Fluctuations of the giant of Poisson random graphs," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002558
    DOI: 10.1016/j.spa.2025.104811
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    References listed on IDEAS

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    1. Galen R. Shorack, 1979. "The weighted empirical process of row independent random variables with arbitrary distribution functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 33(4), pages 169-189, December.
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