Orientation in Poisson Cluster Processes via Imaginary Bispectra
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917490437652480 |
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| author | Kresin, Conor Tang, Yifu Baeumer, Boris Wang, Ting |
| author_facet | Kresin, Conor Tang, Yifu Baeumer, Boris Wang, Ting |
| contents | We study what remains detectable about one-sided Poisson cluster processes after cluster orientation is erased. We construct matched reversible cluster nulls preserving intensity and the full Bartlett spectrum, showing that second-order structure alone need not identify temporal direction. For stationary Poisson branching clusters, we derive the Fourier--Stieltjes transform of the reduced third cumulant and show that, in the $L^1$ third-cumulant regime, a nonzero imaginary factorial bispectrum certifies orientation. We also give explicit orientation-erased nulls, reversible spectral matches for monotone Hawkes kernels, and finite-window third-order orientation contrasts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orientation in Poisson Cluster Processes via Imaginary Bispectra Kresin, Conor Tang, Yifu Baeumer, Boris Wang, Ting Probability Statistics Theory 60G55, 60G10, 62M15 We study what remains detectable about one-sided Poisson cluster processes after cluster orientation is erased. We construct matched reversible cluster nulls preserving intensity and the full Bartlett spectrum, showing that second-order structure alone need not identify temporal direction. For stationary Poisson branching clusters, we derive the Fourier--Stieltjes transform of the reduced third cumulant and show that, in the $L^1$ third-cumulant regime, a nonzero imaginary factorial bispectrum certifies orientation. We also give explicit orientation-erased nulls, reversible spectral matches for monotone Hawkes kernels, and finite-window third-order orientation contrasts. |
| title | Orientation in Poisson Cluster Processes via Imaginary Bispectra |
| topic | Probability Statistics Theory 60G55, 60G10, 62M15 |
| url | https://arxiv.org/abs/2605.13004 |