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arXiv · 2008.04398

Matching for random systems with an application to minimal weight expansions

Karma Dajani·Charlene Kalle·Marta Maggioni
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Abstract

We extend the notion of matching for one-dimensional dynamical systems to random matching for random dynamical systems on an interval. We prove that for a large family of piecewise affine random systems of the interval the property of random matching implies that any invariant density is piecewise constant. We further introduce a one-parameter family of random dynamical systems that produce signed binary expansions of numbers in the interval [-1,1]. This family has random matching for Lebesgue almost every parameter. We use this to prove that the frequency of the digit 0 in the associated signed binary expansions never exceeds 1/2.

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Karma Dajani, Charlene Kalle, Marta Maggioni. 2020-08-10. Matching for random systems with an application to minimal weight expansions. https://doi.org/10.1088/1361-6544/abebc6

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