×

zbMATH — the first resource for mathematics

Normal fluctuations and the FKG inequalities. (English) Zbl 0429.60096

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
81P20 Stochastic mechanics (including stochastic electrodynamics)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baker, G.A., Jr., Krinsky, S.: Renormalization group structure for translationally invariant ferromagnets. J. Math. Phys.18, 590-607 (1977)
[2] Battle, G.A., Rosen, L.: The FKG inequality for the Yukawa2 quantum field theory. Preprint, Univ. of British Columbia (1979)
[3] Ellis, R.S., Newman, C.M.: Fluctuationes in Curie-Weiss exemplis. In: Mathematical problems in theoretical physics. Dell’Antonio, G. Doplicher, S., Jona-Lasinio, G. (eds.). Berlin, Heidelberg, New York: Springer 1978
[4] Esary, J., Proschan, F., Walkup, D.: Association of random variables with applications. Ann. Math. Stat.38, 1466-1474 (1967) · Zbl 0183.21502
[5] Feller, W.: An introduction to probability theory and its applications, Vol. II, 2nd ed. New York: Wiley 1966 · Zbl 0138.10207
[6] Fortuin, C., Kastelyn, P., Ginibre, J.: Correlation inequalities on some partially ordered sets. Commun. Math. Phys.22, 89-103 (1971) · Zbl 0346.06011
[7] Gallavotti, G., Jona-Lasinio, G.: Limit theorems for multidimensional Markov processes. Commun. Math. Phys.41, 301-307 (1975) · Zbl 0343.60043
[8] Gallavotti, G., Martin-Löf, A.: Block-spin distributions for short range attractive Ising models. Nuovo Cimento25B, 425-441 (1975)
[9] Guerra, F., Rosen, L., Simon, B.: TheP(?)2 Euclidean quantum field theory as classical statistical mechanics. Ann. Math.101, 111-259 (1975)
[10] Harris, T.E.: A lower bound for the critical probability in a certain percolation process. Proc. Camb. Phil. Soc.59, 13-20 (1960) · Zbl 0122.36403
[11] Iagolnitzer, D., Souillard, B.: Lee-Yang theory and normal fluctuations. Phys. Rev. B19, 1515-1518 (1979)
[12] Iagolnitzer, D., Souillard, B.: Random fields and limit theorems. To appear in the proceedings of the Estergom 1979 Conference on ?Random fields: rigorous results in statistical mechanics and quantum field theory?
[13] Jona-Lasinio, G.: Probabalistic approach to critical behavior. In: New developments in quantum field theory and statistical mechanics. Lévy, M., Mitter, P. (eds.). New York: Plenum 1977
[14] Kemperman, J.H.B.: On the FKG-inequalities for measures on a partially ordered space. Indag. Math.39, 313-331 (1977) · Zbl 0384.28012
[15] Lebowitz, J.: Bounds on the correlations and analyticity properties of ferromagnetic Ising spin systems. Commun. Math. Phys.28, 313-321 (1972)
[16] Lebowitz, J.: GHS and other inequalities. Commun. Math. Phys.35, 87-92 (1974)
[17] Lehman, E.L.: Some concepts of dependence. Ann. Math. Stat.37, 1137-1153 (1966) · Zbl 0146.40601
[18] Newman, C.M.: Inequalities for Ising models and field theories which obey the Lee-Yang theorem. Commun. Math. Phys.41, 1-9 (1975)
[19] Newman, C.M.: Moment inequalities for ferromagnetic Gibbs distributions. J. Math. Phys.16, 1956-1959 (1975)
[20] Newman, C.M.: Critical point inequalities and scaling limits. Commun. Math. Phys.66, 181-196 (1979) · Zbl 0414.60095
[21] Newman, C.M., Schulman, L.S.: Infinite clusters in percolation models (in preparation) · Zbl 0509.60095
[22] Newman, C.M., Wright, A.L.: An invariance principle for certain dependent sequences (in preparation) · Zbl 0465.60009
[23] Simon, B.: Correlation inequalities and the mass gap inP(?)2. I. Domination by the two point function. Commun. Math. Phys.31, 127-136 (1973) · Zbl 1125.81313
[24] Simon, B.: TheP(?)2 Euclidean (quantum) field theory. Princeton: Princeton University Press 1974
[25] Wells, D.R.: Some moment inequalities and a result on multivariate unimodality. Indiana University Ph. D. Thesis, 1977
[26] Wilson, K.G., Fischer, M.E.: Critical exponents in 3.99 dimensions. Phys. Rev. Lett.28, 240-243 (1972)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.