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  1. Diffusion budgets for contact-freezing lattice ellipsoidsScott SchubrEdition 2 · 2026-11-02 Public
  2. Stable star marginals and strict edge correlations for random forestsScott SchubrEdition 3 · 2026-11-02 Public
  3. Covariance confidence bounds and parity certificates for stable count lawsScott SchubrEdition 3 · 2026-11-02 Public
  4. Sharp collision criteria for frozen color histogramsScott SchubrEdition 3 · 2026-11-02 Public
  5. Finite Persistent Memory in Exact Sampling: Countable Rigidity and Algebraic Memory BoundsScott SchubrEdition 3 · 2026-11-02 Public
  6. Sharp transport identification with unknown Gaussian covarianceScott SchubrEdition 3 · 2026-11-01 Public
  7. Statistical inference for empirical heat-kernel Sinkhorn metricsScott SchubrEdition 5 · 2026-11-01 Public
  8. First-Hit Stopping and Bias-Corrected Score Inference in Dimension ThreeScott SchubrEdition 5 · 2026-11-01 Public
  9. Dimension thresholds for log-concavity of normalized mixed momentsScott SchubrEdition 3 · 2026-10-31 Public
  10. Purity frontiers and optimal copy complexity for qutrit stabilizer measurementsScott SchubrEdition 2 · 2026-10-30 Public
  11. Mixing-weight entropy concavity near the Gaussian below one-half signalScott SchubrEdition 3 · 2026-10-30 Public
  12. Covariance-Spectrum Certificates for Homogeneous Stable Count LawsScott SchubrEdition 8 · 2026-10-30 Public
  13. Joint inclusion bounds for random greedy matroid basesScott SchubrEdition 1 · 2026-10-29 Public
  14. Residual Certificates and Empirical Sharpness for Entropic Self-Transport ScoresScott SchubrEdition 2 · 2026-10-27 Public
  15. Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-TransportScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

Diffusion budgets for contact-freezing lattice ellipsoids

Scott Schubr

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Abstract

We study bounded-covariance matrix martingales whose ellipsoids acquire and retain lattice contacts. On a common set of Haar lattices of probability tending to one, we bound the total nonnegative gain in a heat-occupation frame by the time-averaged square-root diffusion cost. A cost of o(log d) forces this gain to vanish at the horizon (16 log d + 8 log log d + O(1))/d². The bound is uniform over admissible policies on each selected lattice and also gives an averaged-budget theorem. Its proof combines deterministic pair envelopes, radial and angular Haar estimates, same-noise coupling and a potential-weighted restart. Applications include every fixed-strength normalized curvature-preserving tilt and rotating low-rank feedback. We also solve the instantaneous curvature-preserving optimization problem with the same diffusion cost, including noncommuting curvature and occupation operators. For fixed instantaneous operators, matching two-sided bounds give the sharp square-root small-budget law with an explicit linear error.

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