Randomness as uniform distribution modulo 1

VERÓNICA BECHER

Noteroi

Conferencia; Conference on Mathematical Logic, Satellite event for the International Congress of Mathematicians 2018; 2018

Sociedade Brasileira de Lógica and DLMPST/IUHPST

Abstract: How is algorithmic randomness related to the classical theory of uniform distribution? We study Martin-Löf randomness for real numbers in terms of uniform distribution of sequences. We present a necessary condition for a real number to be Martin-Löf random, and a strengthening of that condition which is sufficient for Martin-Löf randomness. For this strengthening we define a notion of uniform distribution relative to the computably enumerable open subsets of the unit interval. We call the notion Sigma^0_1-uniform distribution.This is joint work with Serge Grigorieff and Theodore Slaman.