Deviation and concentration inequalities for dynamical systems with subexponential decay of correlation.

The paper’s Theorem 4.1 states exactly the desired concentration bound for separately Hölder K under stretched-exponential return times, with the denominator κ(∑ L_i^2 + 1 + t^{2−γ}) (see Theorem 4.1 and its proof outline via the Young tower, reversed martingale differences, and the Fan–Grama–Liu inequality) . The candidate solution follows the same blueprint: lift to the Young tower, perform the reversed-martingale decomposition, control the key exponential-moment/variance term, and apply the Fan–Grama–Liu deviation inequality to obtain the same inequality. The only minor omissions are the “wlog small Lipschitz constants” reduction (sup L_i ≤ ε0) used in the paper and that the paper directly controls u_n = ||∑ E[D_p^2 e^{(D_p^+)^γ}|F_{p+1}]||_∞ rather than separating variance and tails, but these are largely presentation differences, not substantive gaps, and lead to the same bound .