On the Asymptotics of the Finite-Perimeter Partition Function of   Two-Dimensional Lattice Vesicles
  We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q^A, in the inflated regime, q>1. The approach q->1^+ of the asymptotic form is examined. 
Thomas Prellberg and Aleksander L. Owczarek