Expected number density of critical points of smooth Gaussian random fields in arbitrary dimensions

arXiv:2607.23903 · math.ST, astro-ph.CO, math.PR · Submitted 2026-07-27 · Read on arXiv

Satoshi Kuriki, Takahiko Matsubara, Satoshi Iso

math.ST, astro-ph.CO, math.PR

Submitted: 2026-07-27

Comments: 25 pages, 1 figure

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Non-Gaussianity — 2× in this paper · explained in 2 episodes
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Abundance — 1× in this paper · explained in 1 episode
• Anisotropy — 1× in this paper · explained in 3 episodes
• Bispectrum — 1× in this paper · explained in 3 episodes
• Primordial non-Gaussianity — 1× in this paper · explained in 2 episodes

Sources

• Expected Euler characteristic method for the largest eigenvalue: (Skew-)orthogonal polynomial approach

Related papers

• Conformal Prediction for Dyadic Regression Under Complex Missingness
• Sharp Asymptotic Theory of Maximum Likelihood Estimation for Gaussian Processes with an RBF Kernel
• Bentkus-type asymptotic e-values
• High-Dimensional Asymptotics of Differentially Private PCA
• A proximal gradient algorithm for composite log-concave sampling
• KL Convergence Guarantees for Score diffusion models under minimal data assumptions