Research Article · Preprint Mathematics
Diffusion budgets for contact-freezing lattice ellipsoids
- Primary subject
- Mathematics
- Subject subfields
- Probability and Statistics · Geometry and Optimal Transport · Optimization and Control
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
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.
Scope of the work
Uniform diffusion-budget bounds for admissible bounded-covariance contact-freezing lattice ellipsoids, with heat-occupation gain, averaged budgets and exact instantaneous curvature-preserving optimization.
Reproduction notes
The package contains editable source, build instructions and numerical demonstrations accompanying the analytic proofs.
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Cite this edition
Scott Schubr. (2026). Diffusion budgets for contact-freezing lattice ellipsoids (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/diffusion-budgets-contact-freezing-lattice-ellipsoids/v/1
BibTeX
@techreport{luminary_diffusion_budgets_contact_freezing_lattice_ellipsoids_v1,
title = {Diffusion budgets for contact-freezing lattice ellipsoids},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/diffusion-budgets-contact-freezing-lattice-ellipsoids/v/1}
}Loading discussion…