Critical Points of Chi-Fields

Domenico Marinucci; Michele Stecconi

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arXiv · 2409.20129

Critical Points of Chi-Fields

Domenico Marinucci·Michele Stecconi

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Abstract

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.

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Domenico Marinucci, Michele Stecconi. 2024-09-30. Critical Points of Chi-Fields. https://arxiv.org/abs/2409.20129

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