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This is a Quantitative Study study.

September 23, 2025Open Access

A tail bound for cumulant series for complex functions of independent random variables

Key Points

Truncation error bounds for cumulant series in complex functions were established, enhancing previous findings.
Application examples include a Berry-Esseen bound and Edgeworth expansions for specific random graph structures.
This research extends prior work from real to complex functions, showing significant breadth in the theoretical framework.
The study also covers enumeration techniques for regular graphs, expanding utility in combinatorial contexts.

Abstract

We obtain explicit bounds on the truncation error of the cumulant series of a bounded complex function of a random vector with independent components. The bounds are based on multidimensional differences. This extends the theory of the author with Brendan McKay and Rui-Ray Zhang (J. Combin. Th., Ser. B, 2025) from real functions to complex functions. We demonstrate some initial applications including a Berry--Esseen bound, an Edgeworth expansion for triangles in random graphs, and enumeration of regular graphs.

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Cite This Study

Mikhail Isaev (Sat,) studied this question.

synapsesocial.com/papers/68d4764731b076d99fa6e00a https://doi.org/https://doi.org/10.48550/arxiv.2508.16952