In this short note we collect together known results on the use of random matrix theory (RMT) in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and secondly it appears to be an effective tool to find...

We consider a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been conjectured. Moreover, an equality between the (asymptotic of the)...

We propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer coefficients. This yields an algebraic value...