Long-time nonequilibrium fluctuations of the hard-sphere gas (finite-dimensional laws)
For a deterministic grand-canonical hard-sphere gas in with smooth initial density having summable Gaussian bounds on it and its gradient, on every where the Boltzmann solution has uniform Gaussian velocity decay, the empirical measure centered at its exact microscopic expectation and scaled by has finite-dimensional distributions converging to those of the Gaussian solution of the linear fluctuating Boltzmann equation. It does not prove process-level convergence or tightness, does not treat periodic domains (the BGSS setting) or potentials, and assumes the regular kinetic solution exists.
Exact FrontierDelta
Scope and record
Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Long-time nonequilibrium fluctuations of the hard-sphere gas (finite-dimensional laws) · Long-time hard-sphere fluctuations
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Unreleased internal OpenAI model
Long-time Boltzmann-Grad limit for stable finite-range radial potentials evidence for this event
VibeMathed record: Long-time nonequilibrium fluctuations of the hard-sphere gas (finite-dimensional laws) evidence for this event
Deng-Hani-Ma, Long time derivation of the Boltzmann equation (arXiv 2408.07818) evidence for this event
For a deterministic grand-canonical hard-sphere gas in with smooth initial density having summable Gaussian bounds on it and its gradient, on every where the Boltzmann solution has uniform Gaussian velocity decay, the empirical measure centered at its exact microscopic expectation and scaled by has finite-dimensional distributions converging to those of the Gaussian solution of the linear fluctuating Boltzmann equation. It does not prove process-level convergence or tightness, does not treat periodic domains (the BGSS setting) or potentials, and assumes the regular kinetic solution exists. parent of this event
Companion: Hard-sphere fluctuations on the regular Boltzmann lifespan evidence for this event
Long-time nonequilibrium fluctuations of the hard-sphere gas (finite-dimensional laws) parent of this event
Act on this frontier