Critical Points of Chi-Fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910625173602304 |
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| author | Marinucci, Domenico Stecconi, Michele |
| author_facet | Marinucci, Domenico Stecconi, Michele |
| contents | We give here a semi-analytic formula for the density of critical values for chi random fields on a general manifold. The result uses Kac-Rice argument and a convenient representation for the Hessian matrix of chi fields, which makes the computation of their expected determinant much more feasible. In the high-threshold limit, the expression for the expected value of critical points becomes very transparent: up to explicit constants, it amounts to Hermite polynomials times a Gaussian density. Our results are also motivated by the analysis of polarization random fields in Cosmology, but they might lead to applications in many different environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical Points of Chi-Fields Marinucci, Domenico Stecconi, Michele Probability Mathematical Physics Differential Geometry 60G60, 33C55, 53C65, 58K05 We give here a semi-analytic formula for the density of critical values for chi random fields on a general manifold. The result uses Kac-Rice argument and a convenient representation for the Hessian matrix of chi fields, which makes the computation of their expected determinant much more feasible. In the high-threshold limit, the expression for the expected value of critical points becomes very transparent: up to explicit constants, it amounts to Hermite polynomials times a Gaussian density. Our results are also motivated by the analysis of polarization random fields in Cosmology, but they might lead to applications in many different environments. |
| title | Critical Points of Chi-Fields |
| topic | Probability Mathematical Physics Differential Geometry 60G60, 33C55, 53C65, 58K05 |
| url | https://arxiv.org/abs/2409.20129 |