The Asymptotic Distribution of the Scaled Remainder for Pseudo Golden Ratio Expansions of a Continuous Random Variable

Let X = ∑ k = 1 ∞ X k β - k be the (greedy) base- β expansion of a continuous random variable X on the unit interval where β is the positive solution to β n = 1 + β + ⋯ + β n - 1 for an integer n ⩾ 2 (i.e., β is a generalization of the golden mean corresponding to n = 2 ). We study the asymptotic di...

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