تقرير
Periodic points of a $p$-adic operator and their $p$-adic Gibbs measures
| العنوان: | Periodic points of a $p$-adic operator and their $p$-adic Gibbs measures |
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| المؤلفون: | Rozikov, U. A., Sattarov, I. A., Tukhtabaev, A. M. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, Mathematics - Number Theory, Mathematics - Probability, 82B26 (12J12 46S10 60K35) |
| الوصف: | In this paper we investigate generalized Gibbs measure (GGM) for $p$-adic Hard-Core(HC) model with a countable set of spin values on a Cayley tree of order $k\geq 2$. This model is defined by $p$-adic parameters $\lambda_i$, $i\in \mathbb N$. We analyze $p$-adic functional equation which provides the consistency condition for the finite-dimensional generalized Gibbs distributions. Each solutions of the functional equation defines a GGM by $p$-adic version of Kolmogorov's theorem. We define $p$-adic Gibbs distributions as limit of the consistent family of finite-dimensional generalized Gibbs distributions and show that, for our $p$-adic HC model on a Cayley tree, such a Gibbs distribution does not exist. Under some conditions on parameters $p$, $k$ and $\lambda_i$ we find the number of translation-invariant and two-periodic GGMs for the $p$-adic HC model on the Cayley tree of order two. Comment: 16 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.04379 |
| رقم الأكسشن: | edsarx.2207.04379 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |