We give examples of piecewise linear random interval maps satisfying arcsine and Darling–Kac laws, which are analogous to Thaler’s arcsine and Aaronson’s Darling–Kac laws for the Boole transformation. They are constructed by random switch of two piecewise linear maps with attracting or repelling fixed points, which behave as if they were indifferent fixed points of a deterministic map.

中文翻译：

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分段线性随机区间映射的反正弦和 Darling–Kac 定律

我们给出了满足反正弦和 Darling–Kac 定律的分段线性随机区间映射的示例，这类似于布尔变换的 Thaler 反正弦和 Aaronson 的 Darling–Kac 定律。它们是由两个具有吸引或排斥不动点的分段线性映射的随机切换构成的，它们的行为就好像它们是确定性映射的无关不动点一样。