LARGE DEVIATION PRINCIPLES FOR PERIODIC POINTS OF THE DYCK SHIFT

The paper proves a level-2 LDP for empirical measures built from Dyck-shift periodic points, identifies the explicit (non-convex) rate function I, and pinpoints the two MMEs as minimizers. The proof hinges on Krieger-type Borel embeddings of two full shifts into the Dyck shift, establishing LDPs on the embedded subsystems and then unifying them via a mixture decomposition. All key steps are rigorously supplied, including exponential negligibility of the neutral class, a contraction argument, and closedness of the effective domains. By contrast, the model’s solution relies on an incorrect claim of a bijection between the Dyck-shift multiplier classes and all periodic points of a full shift and on unsourced asymptotics (#Pern ≈ 2(M+1)^n), which the paper neither assumes nor needs. Hence the model’s argument is not correct as stated, even though its final conclusions match the paper.