Regularization of a stationary point process by a stationary increments perturbation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910030118256640 |
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| author | Thomassey, Loïc Lachièze-Rey, Raphaël Shapira, Assaf |
| author_facet | Thomassey, Loïc Lachièze-Rey, Raphaël Shapira, Assaf |
| contents | We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that the dependency between distant points is weakened; and the potential peaks in the spectrum (or Bragg peaks), reminiscent of a periodic behavior, are erased. We use this procedure to efficiently generate a hyperuniform point process in dimension 1 using a fractional Brownian Motion; simulating n points with complexity n log(n). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularization of a stationary point process by a stationary increments perturbation Thomassey, Loïc Lachièze-Rey, Raphaël Shapira, Assaf Probability We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that the dependency between distant points is weakened; and the potential peaks in the spectrum (or Bragg peaks), reminiscent of a periodic behavior, are erased. We use this procedure to efficiently generate a hyperuniform point process in dimension 1 using a fractional Brownian Motion; simulating n points with complexity n log(n). |
| title | Regularization of a stationary point process by a stationary increments perturbation |
| topic | Probability |
| url | https://arxiv.org/abs/2602.19773 |