2105.11377
Local mixing of one-parameter diagonal flows on Anosov homogeneous spaces
Michael Chow, Pratyush Sarkar
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves the local mixing and correlation limit exactly as stated, using the A-ergodic decomposition of the BMS measure and a refined spectral/transfer-operator analysis to obtain the t^{-(r-1)/2} normalization and a constant κ_v independent of components; the candidate solution outlines the same decomposition-plus-local-mixing strategy and arrives at the identical limit. Minor imprecisions in the model (e.g., on finiteness of components and non-arithmeticity justifications) do not affect correctness.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
This manuscript proves a broad and sharp local mixing theorem for diagonal flows on Anosov homogeneous spaces, covering all interior directions of the limit cone and yielding refined correlation asymptotics with concrete normalizations. The techniques are thoughtfully adapted to higher rank via an innovative transfer-operator-with-holonomy framework and careful coding. The results are important and appear correct. Some improvements in exposition (clarifying normalizations, highlighting the finiteness of ergodic components, and summarizing the role of M\_Γ) would further enhance accessibility.