Estimate of convergence rate in local limit theorem for the particle number in spin systems

For classical lattice spin systems with vacuum, an estimate is obtained of the convergence rate in a local limit theorem for the number of particles in a region A. The estimate has the order of the square rooot of the volume of A.Institute of Mathematics, Armenian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 3, pp. 497–512, June, 1993.