期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2018
卷号：80
期号：2
页码：356-384
DOI：10.1007/s13171-017-0117-3
语种：English
出版社：Indian Statistical Institute
摘要：The Sigma function, which is the sum of the squares of the number of occurrences of every factor, is a criterion of randomness, measuring specially the uniformity of the block distribution. An infinite word whose prefixes attain asymptotically the smallest possible value of it is called Sigma-random. We prove that the Champernowne word is Sigma-random. We also consider less complex words which have values with asymptotically larger order, Sturmian words and almost 0-words.
关键词：Randomness criterion ; Champernowne number ; Sturmian word
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