Semi-classical analysis of non self-adjoint transfer matrices in   statistical mechanics. I
  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. 
Margherita Disertori and Sasha Sodin
math-ph math.MP math.SP