论文信息 - Measures of maximal entropy for random -expansions

Measures of maximal entropy for random -expansions

Let > 1 be a non-integer. We consider -expansions of the form P 1=1 di/ i , where the digits(di)i 1 are generated by means of a Borel mapK defined on {0, 1} N ◊(0,b c/( 1)). We show thatK has a unique mixing measure of maximal entropy with marginal measure an infinite convolution of Bernoulli measures. Furthermore, under the measure the digits (di)i 1 form a uniform Bernoulli process. In case 1 has a finite greedy expansion with positive coefficients, the measure of maximal entropy is Markov. We also discuss the uniqueness of -expansions.

Karma Dajani | Martijn de Vries | M. D. Vries | K. Dajani

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