Poisson approximation of the largest gaps between zeros of a stationary Gaussian process
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918516296253440 |
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| author | Feng, Renjie Muirhead, Stephen |
| author_facet | Feng, Renjie Muirhead, Stephen |
| contents | We study the largest gaps between successive zeros of a smooth stationary Gaussian process. Our main result is that, if correlations decay at least polynomially, then after suitable rescaling of the locations and sizes of the largest gaps in a growing interval, the resulting joint process converges to a Poisson point process. The main novel step in the proof is to establish an approximate splitting property, with multiplicative error, for gap events in well-separated intervals; notably we achieve this for processes with arbitrarily slow polynomial decay of correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poisson approximation of the largest gaps between zeros of a stationary Gaussian process Feng, Renjie Muirhead, Stephen Probability We study the largest gaps between successive zeros of a smooth stationary Gaussian process. Our main result is that, if correlations decay at least polynomially, then after suitable rescaling of the locations and sizes of the largest gaps in a growing interval, the resulting joint process converges to a Poisson point process. The main novel step in the proof is to establish an approximate splitting property, with multiplicative error, for gap events in well-separated intervals; notably we achieve this for processes with arbitrarily slow polynomial decay of correlations. |
| title | Poisson approximation of the largest gaps between zeros of a stationary Gaussian process |
| topic | Probability |
| url | https://arxiv.org/abs/2605.22146 |