A NONSTANDARD-ANALYTIC PROOF OF A THEOREM REGARDING NONCOMMUTATIVE ERGODIC OPTIMIZATIONS

Aidan Young

correcthigh confidence

Category: math.DS
Journal tier: Note/Short/Other
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves the stated limit formula via a nonstandard-analysis construction of an invariant state and a quotient-by-ker(ι) reduction; the candidate gives a standard C*-algebraic proof by averaging near-norming states along a Følner sequence and passing to invariant weak* limits. Both arguments are valid and reach the same conclusion. The paper’s “ergodic” assumption is unused (hence superfluous), and there is a minor typographical slip in the definition of f_x, but neither affects correctness.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} note/short/other

\textbf{Justification:}

The paper gives a clean nonstandard-analysis proof of a limit formula in noncommutative ergodic optimization. The key ideas are sound and the execution is essentially correct. Edits are limited to clarifying a minor typographical error (variable in f\_x) and removing or justifying an unused ergodicity assumption; after these, the note would be a tidy, useful contribution.