ICC   25427
INSTITUTO DE INVESTIGACION EN CIENCIAS DE LA COMPUTACION
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Randomness and uniform distribution modulo one
Autor/es:
SERGE GRIGORIEFF; THEODORE A. SLAMAN; VERONICA BECHER
Lugar:
Oberwolfach
Reunión:
Workshop; "Computability Theory'',workshop; 2018
Institución organizadora:
Mathematisches Forschungsinstitut Oberwolfach
Resumen:
Abstract: How is the notion of randomness of algorithmic information theory related to the notion of uniform distribution of number theory? In this talk we elaborate the definition of Martin-Löf randomness for real numbers in terms of uniform distribution of sequences. First, we identify a necessary condition for a real number to be random, in terms of classical uniform distribution. Then, we introduce a notion of uniform distribution relative to a computable sequence of open intervals with rational endpoints. We call the notion Sigma^0_1-uniform distribution. Based on this notion we give a sufficient condition for a real number to be random. This is Joint work with Serge Grigorieff.