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  1. Diffusion budgets for contact-freezing lattice ellipsoidsScott SchubrEdition 1 · 2026-10-27 Public
  2. Residual Certificates and Empirical Sharpness for Entropic Self-Transport ScoresScott SchubrEdition 2 · 2026-10-27 Public
  3. Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-TransportScott SchubrEdition 2 · 2026-10-27 Public
  4. Statistical inference for empirical heat-kernel Sinkhorn metricsScott SchubrEdition 3 · 2026-10-27 Public
  5. Sharp collision criteria for frozen color histogramsScott SchubrEdition 2 · 2026-10-27 Public
  6. Covariance confidence bounds and parity certificates for stable count lawsScott SchubrEdition 2 · 2026-10-27 Public
  7. Local and eventual mixing-weight entropy concavity under Gaussian smoothingScott SchubrEdition 2 · 2026-10-27 Public
  8. First-Hit Stopping and Bias-Corrected Score Inference in Dimension ThreeScott SchubrEdition 3 · 2026-10-27 Public
  9. Degree laws and edge correlations for random forestsScott SchubrEdition 2 · 2026-10-27 Public
  10. Covariance-Spectrum Certificates for Homogeneous Stable Count LawsScott SchubrEdition 7 · 2026-10-27 Public
  11. Finite Persistent Memory in Exact Sampling: Countable Rigidity and Algebraic Memory BoundsScott SchubrEdition 2 · 2026-10-27 Public
  12. Dimension thresholds for log-concavity of normalized mixed momentsScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 1

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.

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