Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical k-Spin Complexity

arXiv:2606.17665 · math.ST, math.PR, stat.ML · Submitted 2026-06-16 · Read on arXiv

Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro

IMT · UDELAR · ICJ, ECL, PSPM, IUF

math.ST, math.PR, stat.ML

Submitted: 2026-06-16

Code: https://github.com/ydecastro/TENSOR-KSS

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

Terminology

• Coherence — 13× in this paper · explained in 2 episodes
• Gaussian Orthogonal Ensemble — 5× in this paper
• Spectral Method — 4× in this paper
• Absorb — 3× in this paper · explained in 1 episode
• Inflation — 2× in this paper · explained in 2 episodes
• Langevin Dynamics — 2× in this paper · explained in 3 episodes
• Monotonicity — 2× in this paper · explained in 2 episodes
• Phase Transition — 2× in this paper · explained in 3 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Actor — 1× in this paper · explained in 3 episodes
• Admissibility — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Monte Carlo Sampling — 1× in this paper · explained in 2 episodes
• Sample Complexity — 1× in this paper · explained in 20 episodes
• Spectral Signature — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

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