Quasiparticle kinetic theory for Calogero models

The inverse problem method is tested for a class of monomer-dimer statistical \udmechanics models that contain also an attractive potential and display a \udmean-field critical point at a boundary of a coexistence line. The inversion is \udobtained by analytically identifying the parameters in terms of the correlation \udfunctions and via the maximum-likelihood method. The precision is tested in \udthe whole phase space and, when close to the coexistence line, the algorithm is \udused together with a clustering method to take care of the underlying possible \udambiguity of the inversion