Pólya Urn with Memory Kernel and Asymptotic Behaviors of Autocorrelation Function
| العنوان: | Pólya Urn with Memory Kernel and Asymptotic Behaviors of Autocorrelation Function |
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| المؤلفون: | Shintaro Mori, Masato Hisakado, Kazuaki Nakayama |
| المصدر: | Journal of the Physical Society of Japan. 90 |
| بيانات النشر: | Physical Society of Japan, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Statistics::Theory, Stochastic process, Autocorrelation, General Physics and Astronomy, Astrophysics::Cosmology and Extragalactic Astrophysics, Combinatorics, Mathematics::Probability, Physics - Data Analysis, Statistics and Probability, Polya urn, Kernel (statistics), Ball (bearing), Astrophysics::Solar and Stellar Astrophysics, Statistics::Methodology, Condensed Matter - Statistical Mechanics, Mathematics |
| الوصف: | P\'{o}lya urn is a stochastic process in which balls are randomly drawn from an urn of red and blue balls, and balls of the same color as the drawn balls are added. The probability of a ball of a certain color being drawn is equal to the percentage of balls of that color in the urn. We introduce arbitrary memory kernels to modify this probability. If the memory kernel decays exponentially, it is a stationary process and is mean-reverting. If the memory kernel decays by a power-law, a phase transition occurs and the asymptotic behavior of the autocorrelation function changes. An auxiliary field variable is introduced to transform the process Markovian and the field obeys a multivariate Ornstein-Uhlenbeck process. The exponents of the power law are estimated for the decay of the leading and subleading terms of the autocorrelation function. It is shown that the power law exponents changes discontinuously at the critical point. Comment: 22 pages, 1 figure |
| تدمد: | 1347-4073 0031-9015 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8692c12e4943c3cb386215162b63f107 https://doi.org/10.7566/jpsj.90.114010 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....8692c12e4943c3cb386215162b63f107 |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Scitation. | تدمد: | 13474073 00319015 |
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