Long-time Boltzmann-Grad limit for stable finite-range radial potentials

Theorem 1: for a stable finite-range radial potential, a grand-canonical initial law with pair exclusion and $C^1$ density with spatially summable Gaussian bounds on it and its gradient, and any $T$ for which the Boltzmann equation with that potential's scattering has a classical solution with uniform Gaussian velocity bound on $[0,T]$ , all fixed-order rescaled factorial marginals converge in $L^1$ to $f(t)^{\otimes s}$ uniformly on $[0,T]$ ; empirical averages converge in probability. It assumes, rather than proves, existence of the regular kinetic solution, so it gives no global-in-time statement, and it does not treat long-range or non-radial potentials or give a rate.

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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 Boltzmann-Grad limit for stable finite-range radial potentials · Long-time Boltzmann limit, potentials

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VibeMathed record: Long-time Boltzmann-Grad limit for stable finite-range radial potentials

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No independent mathematician has checked this yet. Checked here: Theorem 1 of the principal manuscript was read against the further problem as the paper reports it from Deng-Hani-Ma Section 1.4.2. It covers stable radial potentials vanishing beyond unit range, $C^2$ except a possible repulsive singularity at the origin, with attractive wells allowed, for $C^1$ initial densities with summable Gaussian bounds and initial pair exclusion, on every interval where a classical Boltzmann solution with uniform Gaussian decay is assumed to exist. The wording of the Deng-Hani-Ma problem itself was not read here. The proof was not refereed. No Lean formalization exists for this family.

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Long-time Boltzmann-Grad limit for stable finite-range radial potentials

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Companion: Hard-sphere fluctuations on the regular Boltzmann lifespan

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Deng-Hani-Ma, Long time derivation of the Boltzmann equation (arXiv 2408.07818)

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Deng-Hani-Ma, Long time derivation of the Boltzmann equation (arXiv 2408.07818) evidence for this event

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Companion: Hard-sphere fluctuations on the regular Boltzmann lifespan evidence for this event

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