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Randomness Criterion Σ and Its Applications
- Authors
- Kamae, Teturo; Kim, Dong Han; Xue, Yu-Mei
- Issue Date
- Aug-2018
- Publisher
- SPRINGER
- Keywords
- Randomness criterion; Champernowne number; Sturmian word
- Citation
- Sankhya A, v.80, no.2, pp 356 - 384
- Pages
- 29
- Indexed
- SCOPUS
ESCI
- Journal Title
- Sankhya A
- Volume
- 80
- Number
- 2
- Start Page
- 356
- End Page
- 384
- ISSN
- 0976-836X
0976-8378
- Abstract
- 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.
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Related Researcher
- Kim, Dong Han
- College of Education (Department of Mathematics Education)