The giant component of excursion sets of spherical Gaussian ensembles: existence, uniqueness, and volume concentration
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909761500348416 |
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| author | Muirhead, Stephen Wigman, Igor |
| author_facet | Muirhead, Stephen Wigman, Igor |
| contents | We establish the existence and uniqueness of a well-concentrated giant component in the supercritical excursion sets of three important ensembles of spherical Gaussian random fields: Kostlan's ensemble, band-limited ensembles, and the random spherical harmonics. Our main results prescribe quantitative bounds for the volume fluctuations of the giant that are essentially optimal for non-monochromatic ensembles, and suboptimal but still strong for monochromatic ensembles.
Our results support the emerging picture that giant components in Gaussian random field excursion sets have similar large-scale statistical properties to giant components in supercritical Bernoulli percolation. The proofs employ novel decoupling inequalities for spherical ensembles which are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The giant component of excursion sets of spherical Gaussian ensembles: existence, uniqueness, and volume concentration Muirhead, Stephen Wigman, Igor Probability We establish the existence and uniqueness of a well-concentrated giant component in the supercritical excursion sets of three important ensembles of spherical Gaussian random fields: Kostlan's ensemble, band-limited ensembles, and the random spherical harmonics. Our main results prescribe quantitative bounds for the volume fluctuations of the giant that are essentially optimal for non-monochromatic ensembles, and suboptimal but still strong for monochromatic ensembles. Our results support the emerging picture that giant components in Gaussian random field excursion sets have similar large-scale statistical properties to giant components in supercritical Bernoulli percolation. The proofs employ novel decoupling inequalities for spherical ensembles which are of independent interest. |
| title | The giant component of excursion sets of spherical Gaussian ensembles: existence, uniqueness, and volume concentration |
| topic | Probability |
| url | https://arxiv.org/abs/2406.09659 |