KFU. Card publication. Finding exact constants in a Markov model of Zipfs law generation

KAZAN
FEDERAL UNIVERSITY

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- 中文
- ES

FINDING EXACT CONSTANTS IN A MARKOV MODEL OF ZIPFS LAW GENERATION

Form of presentation

Articles in international journals and collections

Year of publication

2017

Язык

английский

Authors, employees of KFU

Bochkarev Vladimir Vladimirovich, author

Lerner Eduard Yulevich, author

Authors, students KFU

Nikiforov Anton Aleksandrovich, author

Pismenskiy Aleksandr Aleksandrovich, author

Bibliographic description in the original language

V.V. Bochkarev, E.Yu. Lerner, A.A. Nikiforov, A.A. Pismenskiy. Finding exact constants in a Markov model of Zipfs law generation // 2017 J. Phys.: Conf. Ser. 936 012028

Annotation

According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent −1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. Combinatorial technique allowed taking into account all the words with probability of more than $e^{-300}$ in case of 2 by 2 of transition probability matrix. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row with weights presenting the elements of presenting the elements of the vector $\pi$ of the stationary distribution of the Markov chain.

Keywords

Zipfs law, power law constants, Markov chain, transition probability matrix, conditional entropy, stationary distribution

The name of the journal

Journal of Physics: Conference Series

URL

http://iopscience.iop.org/article/10.1088/1742-6596/936/1/012028/pdf

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=173627&p_lang=2

Resource files

File name	Size (MB)	Format
Bochkarev_2017_J._Phys.%3A_Conf._Ser._936_012028.pdf	0,27	pdf	show / download
F_Bochkarev_2017_J._Phys.%3A_Conf._Ser._936_012028.pdf	0,27	pdf	show / download
F_Bochkarev_2017_J._Phys.%3A_Conf._Ser._936_012028.pdf	0,27	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bochkarev Vladimir Vladimirovich	ru_RU
dc.contributor.author	Lerner Eduard Yulevich	ru_RU
dc.contributor.author	Nikiforov Anton Aleksandrovich	ru_RU
dc.contributor.author	Pismenskiy Aleksandr Aleksandrovich	ru_RU
dc.date.accessioned	2017-01-01T00:00:00Z	ru_RU
dc.date.available	2017-01-01T00:00:00Z	ru_RU
dc.date.issued	2017	ru_RU
dc.identifier.citation	V.V. Bochkarev, E.Yu. Lerner, A.A. Nikiforov, A.A. Pismenskiy. Finding exact constants in a Markov model of Zipfs law generation // 2017 J. Phys.: Conf. Ser. 936 012028	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=173627&p_lang=2	ru_RU
dc.description.abstract	Journal of Physics: Conference Series	ru_RU
dc.description.abstract	According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent −1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. Combinatorial technique allowed taking into account all the words with probability of more than $e^{-300}$ in case of 2 by 2 of transition probability matrix. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row with weights presenting the elements of presenting the elements of the vector $\pi$ of the stationary distribution of the Markov chain.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Zipfs law	ru_RU
dc.subject	power law constants	ru_RU
dc.subject	Markov chain	ru_RU
dc.subject	transition probability matrix	ru_RU
dc.subject	conditional entropy	ru_RU
dc.subject	stationary distribution	ru_RU
dc.title	Finding exact constants in a Markov model of Zipfs law generation	ru_RU
dc.type	Articles in international journals and collections	ru_RU