Estimate of convergence rate in local limit theorem for the particle number in spin systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 497-512 Cet article a éte moissonné depuis la source Math-Net.Ru

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For classical lattice spin systems with vacuum it is obtained an estimate of the convergence rate in the local limit theorem for the number of particles in a region $\Lambda$. The estimate has an order of the square root of the volume $\Lambda$.
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B. S. Nakhapetian; S. K. Pogosyan. Estimate of convergence rate in local limit theorem for the particle number in spin systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 497-512. http://geodesic.mathdoc.fr/item/TMF_1993_95_3_a6/

[1] Arzumanyan V. A., Nakhapetyan B. C., Pogosyan S. K., TMF, 67:1 (1986), 21–31 | MR

[2] Arzumanyan V. A., Nakhapetyan B. C., Pogosyan S. K., TMF, 81:2 (1989), 175–184 | MR

[3] Arzumanyan V. A., Nakhapetyan B. C., Pogosyan S. K., TMF, 89:2 (1991), 178–189 | MR

[4] Arzumanian V. A., Nahapetian B. S., Pogosian S. K., Acta Applicandae Mathematicae, 22 (1991), 33–53 | MR

[5] Pogosian S. K., “Asymptotic expansion in the local limit theorem for the particle number in the grand canonical ensemble”, Random fields, vol. I, II (Esztergom, 1979), North-Holland, Amsterdam, 1981, 889–913 | MR

[6] Pogosian S. K., Commun. Math. Phys., 95 (1984), 227–245 | DOI | MR | Zbl

[7] Ryuel D., Statisticheskaya mekhanika, Mir, M., 1971

[8] Dobrushin R. L., Teoriya veroyatn. i ee primen., 13:2 (1968), 201–229 | MR | Zbl

[9] Dobrushin R. L., Funkts. analiz i ego prilozh., 4 (1968), 31–43 | Zbl

[10] Nahapetian B. S., Limit theorems and some applications in statistical physics, Teubner-Texte zur Mathematik, Stuttgart-Leipzig, 1991 | MR | Zbl

[11] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965 | MR

[12] Dobrushin R. L., Nakhapetyan B. C., TMF, 20:2 (1974), 223–234 | Zbl