Block distribution in random strings
Annales de l'Institut Fourier, Volume 43 (1993) no. 2, p. 539-549
For almost all infinite binary sequences of Bernoulli trials (p,q) the frequency of blocks of length k(N) in the first N terms tends asymptotically to the probability of the blocks, if k(N) increases like log 1 p N- log 1 p N-ψ(N) (for pq) where ψ(N) tends to +. This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case p=q=1 2.
Pour presque toute suite binaire infinie issue d’un tirage de Bernoulli (p,q) la fréquence des blocs de longueur k(N) dans les N premiers termes tend asymptotiquement vers la probabilité naturelle du bloc, ceci lorsque k(N) croît comme log 1 p N- log 1 p N-ψ(N) (avec pq) où ψ(N) tend vers +. Ce résultat généralise celui de P. Flajolet, P. Kirschenhofer et R.F. Tichy concernant le cas uniforme p=q=1 2.
@article{AIF_1993__43_2_539_0,
     author = {Grabner, Peter J.},
     title = {Block distribution in random strings},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {43},
     number = {2},
     year = {1993},
     pages = {539-549},
     doi = {10.5802/aif.1345},
     zbl = {0778.60023},
     mrnumber = {94d:60044},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1993__43_2_539_0}
}
Grabner, Peter J. Block distribution in random strings. Annales de l'Institut Fourier, Volume 43 (1993) no. 2, pp. 539-549. doi : 10.5802/aif.1345. http://www.numdam.org/item/AIF_1993__43_2_539_0/

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