A construction of a \lambda-Poisson generic sequence.

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. [ABSTRACT FROM AUTHOR]