Local large deviations for periodic infinite horizon Lorentz gases

Ian Melbourne, Françoise Pène, Dalia Terhesiu

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves the stated LLD bound by a Fourier-analytic method on a Young tower, obtaining only Cr (r<2) regularity for eigenvalues and spectral projections and therefore using difference-quotient estimates instead of second derivatives. The candidate solution performs two integrations by parts and invokes second derivatives of the spectral projector Pu (and effectively of μ(Pu 1)), without providing or citing valid C2 bounds. This step is not supported by the known theory and is precisely what the paper avoids by developing Cr, r<2, control. Thus the model’s proof outline is incomplete/incorrect at a crucial step, while the paper’s argument is correct and complete.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper establishes a sharp LLD bound for infinite-horizon Lorentz gases using a carefully crafted Fourier-analytic strategy on a Young tower, obtaining Cr (r<2) control for spectral data and exploiting finite differences to avoid unavailable second derivatives. The argument is rigorous and advances the technical toolkit for nonuniformly hyperbolic systems. Minor clarifications would improve readability.