A Two-Sided Estimate for the Gaussian Noise Stability Deficit
summary
Proves a quantitative two‑sided bound that controls the Gaussian noise‑stability deficit by a centroid metric (norm difference between Gaussian centers) up to explicit constants and a logarithmic factor, turning the previous delta^4 bound into essentially delta^2 ≤ C·epsilon. Proof builds an evolving family of conditioned densities via a martingale Brownian coupling, uses Ito calculus and quadratic variation to compare any set with the corresponding half‑space, and yields robustness for Gaussian isoperimetry and discrete Majority‑is‑Stablest applications.
AI-written summary · about