On Gaussian Self-Similar Random Fields on a 2-Adic Plane

被引：0

作者：

M. D. Missarov

机构：

[1] Kazan Federal University,

来源：

Russian Mathematics | 2020年 / 64卷

关键词：

Gaussian field; p-adic space; scaling transformation; characteristic functional; homogeneous generalized function;

D O I：

暂无

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学科分类号：

摘要：

The article describes a new type of Gaussian fields on a two-dimensional 2-adic space, invariant under the translation group and group of scaling transformations (self-similar random fields). Fields are characterized by quadratic characteristic functionals defined by homogeneous generalized functions on a 2-adic space. The properties of the proposed generalized homogeneous functions are investigated and the positive definiteness of the correlation functionals is proved.

引用

页码：83 / 87

页数：4

共 6 条

[1] Dobrushin RL(1979)Gaussian and their Subordinated Self-Similar Random Generalized Fields Ann. Prob. 7 1-28
[2] Missarov MD(1991)Renormalization group and renormalization theory in p-adic and adelic scalar models Adv. Sov. Math. 3 143-161
[3] Missarov MD(2015)Dynamics of renormalization group in the lower half-plane of the coupling constants of the fermionic hierarchical model Russian Mathematics (Iz. VUZ.) 59 62-66
[4] Shamsutdinov AF(2018)Zone Structure of the Renormalization Group Flow in a Fermionic Hierarchical Model Theor. Math. Phys. 194 377-383
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