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arXiv · 1303.1081

On the Invariant Density of the Random Beta-Transformation

Tom Kempton
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Abstract

We construct a Lebesgue measure preserving natural extension of the random beta-transformation. This allows us to give a formula for the density of the absolutely continuous invariant probability measure, answering a question of Dajani and de Vries, and also to evaluate some estimates on the typical branching rate of the set of beta-expansions of a real number.

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Tom Kempton. 2013-03-05. On the Invariant Density of the Random Beta-Transformation. https://arxiv.org/abs/1303.1081

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