Geodesic
The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 30-33

Voir la notice de l'article provenant de la source Math-Net.Ru

The model of word generation with independent unequal letter probabilities is analyzed in the article. It is proved that the probability $p(r)$ of words of rank $r$ has the power asymptotic behavior. Elementary methods not similar to Conrad and Mitzenmacher ones are used to represent a short proof of the theorem. We derive also an explicit formula of power.
Keywords: Zipf law, monkey model, order statistics, power laws, recursive sequences, functional equations.
Mots-clés : Pascal pyramid 
@article{IVM_2012_12_a2,
     author = {V. V. Bochkarev and E. Yu. Lerner},
     title = {The {Zipf} law for random texts with unequal letter probabilities and the {Pascal} pyramid},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--33},
     publisher = {mathdoc},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_12_a2/}
}
TY  - JOUR
AU  - V. V. Bochkarev
AU  - E. Yu. Lerner
TI  - The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2012
SP  - 30
EP  - 33
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2012_12_a2/
LA  - ru
ID  - IVM_2012_12_a2
ER  - 
%0 Journal Article
%A V. V. Bochkarev
%A E. Yu. Lerner
%T The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2012
%P 30-33
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2012_12_a2/
%G ru
%F IVM_2012_12_a2
V. V. Bochkarev; E. Yu. Lerner. The Zipf law for random texts with unequal letter probabilities and the Pascal pyramid. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 30-33. http://geodesic.mathdoc.fr/item/IVM_2012_12_a2/