A note on small probabilities for spherical random fields at a critical regime

Marco Carfagnini

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arXiv · 2508.08562

A note on small probabilities for spherical random fields at a critical regime

Marco Carfagnini

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Abstract

We consider time-dependent space isotropic and time stationary spherical Gaussian random fields. We establish Chung's law of the iterated logarithm and solve the small probabilities problem. Our results depend on the high-frequency behaviour of the angular power spectrum: the speed of decay of the small ball probability is faster as either the memory parameter or the space-parameter decreases.

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Marco Carfagnini. 2025-08-12. A note on small probabilities for spherical random fields at a critical regime. https://arxiv.org/abs/2508.08562

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