Shadow and percolation II: discrete and continuous landscapes with correlations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909823403032576 |
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| author | Vernotte, David |
| author_facet | Vernotte, David |
| contents | In this paper we consider a discrete or continuous landscape with correlations and we consider a source of light (a sun) at infinity emitting parallel rays of light making a slope l with the horizontal plane. Depending on the value of l some portions of the landscape may be lit by the sun or be in the shadow. Under some assumptions, we show that if l is big enough then there exists a giant component of light. However, if l>0 is small enough and if we are in discrete case, then there exists a giant component of shadow. We relate this problem to the study of the percolation properties of a new random planar field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shadow and percolation II: discrete and continuous landscapes with correlations Vernotte, David Probability In this paper we consider a discrete or continuous landscape with correlations and we consider a source of light (a sun) at infinity emitting parallel rays of light making a slope l with the horizontal plane. Depending on the value of l some portions of the landscape may be lit by the sun or be in the shadow. Under some assumptions, we show that if l is big enough then there exists a giant component of light. However, if l>0 is small enough and if we are in discrete case, then there exists a giant component of shadow. We relate this problem to the study of the percolation properties of a new random planar field. |
| title | Shadow and percolation II: discrete and continuous landscapes with correlations |
| topic | Probability |
| url | https://arxiv.org/abs/2510.03040 |