English

Semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. I

Mathematical Physics 2016-11-10 v3 math.MP Spectral Theory

Abstract

We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer operator is a perturbation of a normal one. Then the transfer operator is studied using methods of semi-classical analysis. In this paper we concentrate on the second step, the main technical result being a semi-classical estimate for powers of an integral operator which is approximately normal.

Keywords

Cite

@article{arxiv.1407.7804,
  title  = {Semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. I},
  author = {Margherita Disertori and Sasha Sodin},
  journal= {arXiv preprint arXiv:1407.7804},
  year   = {2016}
}

Comments

28 pp, improved the presentation