Central limit theorems for the ergodic adding machine

Mordechay B. Levin, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper we find a second class of sequences of random numbers (xn)n=1 (the orbit of the ergodic adding machine) such that the corresponding sequences of zeros and ones 1[0,y) (xx) (n = 1, 2,..., N) satisfy Central Limit Theorems with extremely small standard deviation σN = O(√logN), instead of O(√N), as N - ∞.

Original languageEnglish
Pages (from-to)61-92
Number of pages32
JournalIsrael Journal of Mathematics
StatePublished - 2003


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