ARCSINE LAW FOR CORE RANDOM DYNAMICS

The paper proves a generalized arcsine law for the random core dynamics via a rigorous skew-product/infinite-ergodic approach, verifying Thaler–Zweimüller’s conditions (C1)–(C4) and computing wandering-rate asymptotics using a simple random-walk encoding of the outside-core motion; see the statement of Theorem 1.2 and setup (1.3)–(1.4) with the dyadic partition (Section 3), Lemma 4.4 (random-walk identification), the conditions in Theorem 2.3, and the computations leading to wN(Ỹ) ~ const·N^{1/2} and β = ν(I−1)/(ν(I−1)+ν(I+1)) . The model’s solution gives a different excursion-based proof that is conceptually consistent: it decomposes orbits into i.i.d. heavy-tailed outside excursions (α=1/2), identifies exit-side frequencies from ν, and applies Lamperti’s occupation-time theorem to obtain the same limiting density with b=(1−β)/β; despite a minor parity error in the explicit SSRW hitting-time formula, the tail index and resulting limit law are correct and match the paper’s result .