КФУ. Карточка публикации. Finding exact constants in a Markov model of Zipfs law generation

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FINDING EXACT CONSTANTS IN A MARKOV MODEL OF ZIPFS LAW GENERATION

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2017

Язык

английский

Авторы, сотрудники КФУ

Бочкарев Владимир Владимирович, автор

Лернер Эдуард Юльевич, автор

Авторы, студенты КФУ

Никифоров Антон Александрович, автор

Письменский Александр Александрович, автор

Библиографическое описание на языке оригинала

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

Аннотация

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.

Ключевые слова

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

Название журнала

Journal of Physics: Conference Series

URL

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

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https://repository.kpfu.ru/?p_id=173627

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Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Бочкарев Владимир Владимирович	ru_RU
dc.contributor.author	Лернер Эдуард Юльевич	ru_RU
dc.contributor.author	Никифоров Антон Александрович	ru_RU
dc.contributor.author	Письменский Александр Александрович	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/?p_id=173627	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	Статьи в зарубежных журналах и сборниках	ru_RU