Convergence of Renormalization Group Transformations of Gibbs Random Field | Science Publications

Journal of Mathematics and Statistics

Farida Kachapova¹  Ilias Kachapov¹ 

关键词: Gibbs Measure;    Renormalization Group;    Semi-Invariant;    Thermodymanic Limit;    Weak Dependence;   

DOI  :  10.3844/jmssp.2016.135.151

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group transformation. Here we consider a thermodynamic limit of a lattice model with weak interaction and we use semi-invariants to prove that random fields transformed by renormalization group converge in distribution to an independent field with Gaussian distribution as the distance scale infinitely increases; it is a generalization of the central limit theorem to weakly dependent fields on a lattice.

【 授权许可】

Unknown