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We derive the dominant asymptotic form and the order of the correction termsof the finite-perimeter partition function of self-avoiding polygons on thesquare lattice, which are weighted according to their area A as q^A, in theinflated regime, q>1. The approach q->1^+ of the asymptotic form is examined.Comment: accepted for publication in Communications in Mathematical Physic

On the Asymptotics of the Finite-Perimeter Partition Function of Two-Dimensional Lattice Vesicles