A tail bound for cumulant series for complex functions of independent random variables
Combinatorics
2025-08-29 v2 Probability
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.
Keywords
Cite
@article{arxiv.2508.16952,
title = {A tail bound for cumulant series for complex functions of independent random variables},
author = {Mikhail Isaev},
journal= {arXiv preprint arXiv:2508.16952},
year = {2025}
}