A construction of a lambda-Pooisson generic sequence

VERONICA BECHER; GABRIEL SAC HIMELFARB

MATHEMATICS OF COMPUTATION

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2023

0025-5718

Years ago Zeev Rudnick defined the lambda-Poisson generic sequences as the infinite sequences of symbols in a finite alphabet where the number of occurrences of long words in the initial segments follow the Poisson distribution with parameter lambda. Although almost all sequences, with respect to the uniform measure, are Poisson generic, no explicit instance has yet been given.In this note we give a construction of an explicit lambda-Poisson generic sequence over any alphabet and any positive lambda, except for the case of the two-symbol alphabet, in which it is required that $lambda$ be less than or equal to the natural logarithm of 2. Since lambda-Poisson genericity implies Borel normality, the constructed sequences are Borel normal. The same construction provides explicit instances of Borel normal sequences that are not lambda-Poisson generic.