Higher-order dangers and precisely constructed taxa in models of randomness.

ABSTRACT: The certification, construction, and delineation of individual, infinite-length "random" sequences have been longstanding yet incompletely resolved problems. We address this topic via the study of normal numbers, which often have been viewed as reasonable proxies for randomness, given their limiting equidistribution of subblocks of all lengths. However, limitations arise within this perspective. First, we explicitly construct a normal number that satisfies the law of the iterated logarithm yet exhibits pairwise bias toward repeated values, rendering it inappropriate for any collection of random numbers. Accordingly, we deduce that the evaluation of higher-order block dynamics, even beyond limiting equidistribution and fluctuational typicality, is imperative in proper evaluation of sequenti

SUBMITTER: Pincus S 

PROVIDER: S-EPMC3992646 | biostudies-literature | 2014 Apr

REPOSITORIES: biostudies-literature