Berry's random waves and stationary Poisson line processes share large-domain fluctuation limits in the fractional Gaussian field class with Hurst index H=(1-d)/2 for observables correlated with their second Wiener chaos projection.
Spectral criteria for the asymptotics of local functionals of Gaussian fields and their application to nodal volumes and critical points.Preprint ArXiv: 2501.07356, 2025
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
fields
math.PR 2years
2026 2verdicts
UNVERDICTED 2roles
background 1polarities
background 1representative citing papers
Functionals of infinite-width random neural networks on the sphere exhibit phase transitions in fluctuations as depth grows, converging to a limiting Gaussian field functional, a Gaussian, or a Qth Wiener chaos distribution depending on covariance fixed points.
citing papers explorer
-
Scars in random waves and the FGF 1/2 universality class
Berry's random waves and stationary Poisson line processes share large-domain fluctuation limits in the fractional Gaussian field class with Hurst index H=(1-d)/2 for observables correlated with their second Wiener chaos projection.
-
Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
Functionals of infinite-width random neural networks on the sphere exhibit phase transitions in fluctuations as depth grows, converging to a limiting Gaussian field functional, a Gaussian, or a Qth Wiener chaos distribution depending on covariance fixed points.