dorsal/arxiv
View SchemaHigh-Order Correlation Functions of Binary Multi-Step Markov Chains
| Authors | S. S. Apostolov, Z. A. Mayzelis, O. V. Usatenko, V. A. Yampol'skii |
|---|---|
| Categories | |
| ArXiv ID | physics/0610081 |
| URL | https://arxiv.org/abs/physics/0610081 |
Abstract
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence relations for correlation functions. These methods are applied for two important particular classes of the Markov chains. These classes include the Markov chains with permutative conditional probability functions and the additive Markov chains with the small memory functions. The exciting property of the self-similarity (discovered in Phys. Rev. Lett. 90, 110601 (2003) for the additive Markov chain with the step-wise memory function) is proved to be the intrinsic property of any permutative Markov chain. Applicability of the correlation functions of the additive Markov chains with the small memory functions to calculating the thermodynamic characteristics of the classical Ising spin chain with long-range interaction is discussed.
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"abstract": "Two approaches to studying the correlation functions of the binary Markov\nsequences are considered. The first of them is based on the study of\nprobability of occurring different \u0027\u0027words\u0027\u0027 in the sequence. The other one\nuses recurrence relations for correlation functions. These methods are applied\nfor two important particular classes of the Markov chains. These classes\ninclude the Markov chains with permutative conditional probability functions\nand the additive Markov chains with the small memory functions. The exciting\nproperty of the self-similarity (discovered in Phys. Rev. Lett. 90, 110601\n(2003) for the additive Markov chain with the step-wise memory function) is\nproved to be the intrinsic property of any permutative Markov chain.\nApplicability of the correlation functions of the additive Markov chains with\nthe small memory functions to calculating the thermodynamic characteristics of\nthe classical Ising spin chain with long-range interaction is discussed.",
"arxiv_id": "physics/0610081",
"authors": [
"S. S. Apostolov",
"Z. A. Mayzelis",
"O. V. Usatenko",
"V. A. Yampol\u0027skii"
],
"categories": [
"physics.data-an",
"physics.gen-ph"
],
"title": "High-Order Correlation Functions of Binary Multi-Step Markov Chains",
"url": "https://arxiv.org/abs/physics/0610081"
},
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