The growth statistics of Zipfian ensembles: Beyond Heaps' law

Physica A: Statistical Mechanics and its Applications

Volumn 390, Issue 20, 2011, Pages 3189-3203

  Eliazar, Iddo ^a  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Functional Central Limit Theorems (FCLTs); Growth processes; Heaps curve; Heaps process; Heaps' law; Poisson processes; Power laws; Rank distributions; Zipf's law

Indexed keywords

COMPUTATIONAL LINGUISTICS; POISSON DISTRIBUTION; RANDOM PROCESSES;

FUNCTIONAL CENTRAL LIMIT THEOREM; GROWTH PROCESS; HEAPS CURVE; HEAPS' LAW; POISSON PROCESS; POWER-LAW; RANK DISTRIBUTIONS; ZIPF'S LAW;

STOCHASTIC SYSTEMS;

EID: 79961031117     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2011.05.003     Document Type: Article

References (24)

1. G.K. Zipf Human Behavior and the Principle of Least Effort 1949 Addison-Wesley Cambridge
2. H.S. Heaps Information Retrieval: Computational and Theoretical Aspects 1978 Academic Press Boston
3. C. Cattutoa Proc. Natl. Acad. Sci. 106 2009 10511
4. R. Baeza-Yates, and G. Navarro J. Amer. Soc. Inform. Sci. 51 2000 69
5. D.C. van Leijenhorst, and Th.P. van der Weide Inform. Sci. 170 2005 263
6. M.A. Serrano, A. Flammini, and F. Menczer PLoS ONE 4 2009 e5372
7. L. Lu, Z.K. Zhang, and T. Zhou PLoS ONE 5 2010 e14139
8. F. Auerbach Petermanns Geographische Mitteilungen 59 1913 74
9. J.B. Estoup Gammes Stenographiques 1916 Institut Stenographique de France Paris
10. A.J. Lotka J. Washington Acad. Sci. 16 1926 317
11. M.E.J. Newman Contemp. Phys. 46 2005 323
12. M. Mitzenmacher Internet Math. 1 2004 226
13. R. Albert, and A.L. Barabási Rev. Mod. Phys. 74 2002 47
14. R. Cohen, and S. Havlin Complex Networks: Structure, Robustness and Function 2010 Cambridge University Press Cambridge
15. H. Hu, D. Han, and X. Wang Physica A 389 2010 1065
16. http://www.nslij-genetics.org/wli/zipf/.
17. P. Bak How Nature Works: The Science of Self Organized Criticality 1996 Copernicus New York
18. I. Eliazar Limit laws for Zipf's law J. Phys. A 44 2011 022001
19. J.F.C. Kingman Poisson Processes 1993 Oxford University Press Oxford
20. http://plato.stanford.edu/entries/types-tokens/.
21. Feller An Introduction to Probability Theory and its Applications, Vol. I 1957 Wiley New York
22. L.E. Baum, and P. Billingsley Ann. Math. Stat. 36 1965 1835
23. S. Bernhardsson, L. Rocha, and P. Minnhagen New J. Phys. 11 2009 123015
24. M.D. Donsker Mem. Amer. Math. Soc. 6 1951 1