Application of semi-invariants to proof of the central limit theorem on a lattice

Farida Kachapova; Ilias Kachapov

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arXiv · 1504.06935

Application of semi-invariants to proof of the central limit theorem on a lattice

Farida Kachapova·Ilias Kachapov

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Abstract

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 Ising model with weak interaction and we use semi-invariants to prove that a random field transformed by renormalization group converges 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 the Ising model.

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BibTeX RIS

Farida Kachapova, Ilias Kachapov. 2015-04-27. Application of semi-invariants to proof of the central limit theorem on a lattice. https://arxiv.org/abs/1504.06935

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