A tail bound for cumulant series for complex functions of independent random variables
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918131773997056 |
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| author | Isaev, Mikhail |
| author_facet | Isaev, Mikhail |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A tail bound for cumulant series for complex functions of independent random variables Isaev, Mikhail Combinatorics Probability 05C30, 60F05, 05C80 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. |
| title | A tail bound for cumulant series for complex functions of independent random variables |
| topic | Combinatorics Probability 05C30, 60F05, 05C80 |
| url | https://arxiv.org/abs/2508.16952 |