Inégalités de corrélation sur {-1,1} n et dans ℝ n
Laroche, Étienne
Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993), p. 531-567 / Harvested from Numdam
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@article{AIHPB_1993__29_4_531_0,
     author = {Laroche, \'Etienne},
     title = {In\'egalit\'es de corr\'elation sur $ \lbrace  -1, 1 \rbrace ^n$ et dans $\mathbb {R}^n$},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {29},
     year = {1993},
     pages = {531-567},
     mrnumber = {1251140},
     zbl = {0806.60008},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1993__29_4_531_0}
}

Laroche, Étienne. Inégalités de corrélation sur $ \lbrace  -1, 1 \rbrace ^n$ et dans $\mathbb {R}^n$. Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) pp. 531-567. http://gdmltest.u-ga.fr/item/AIHPB_1993__29_4_531_0/

[1] R.B. Griffiths, Correlations in Ising Ferromagnets I, II, J. of Math. Phys., vol. 8, 1967, p. 478-483; p. 484-489.

[2] D.G. Kelly et S. Sherman, General Griffiths' Inequalities on Correlations in Ising Ferromagnets, J. Math. Phys., vol. 9, 1968, p. 466-484.

[3] C. Fortuin, P. Kastelyn et J. Ginibre, Correlation Inequalities on some Partially Ordered Sets, Comm. in Math. Phys., vol. 22, 1971, p. 89-103. | MR 309498 | Zbl 0346.06011

[4] R.B. Griffiths, C.A. Hurst et S. Sherman, Concavity of Magnetization of an Ising Ferromagnet in a Positive External Field, J. Math. Phys., vol. 11, 1970, p. 790-795. | MR 266507

[5] J.L. Lebowitz, GHS and other Inequalities, Comm. Math. Phys., vol. 35, 1974, p. 87- 92. | MR 339738

[6] R.S. Ellis, Entropy and large Deviations in Statistical Mechanics, Springer-Verlag. | Zbl 0566.60097

[7] H.O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter studies in mathematics. | MR 956646 | Zbl 0657.60122

[8] J. Glimm et A. Jaff, Quantum Physics: a Functional Integral Point of View, Springer-Verlag, 1981. | MR 628000 | Zbl 0461.46051

[9] B. Simon, B, The P(φ)2 Euclidian (Quantum) Field Theory, Princeton Series, in Physics, 1974. | MR 489552 | Zbl 1175.81146

[10] D. Bakry et D. Michel, Sur les inégalités FKG, Preprint.

[11] I. Herbst et L. Pitt, Diffusion Equation Technique in Stochastic Monotonicity and Positive Correlations, Prob. Th. Rel. Fields, vol. 87, 1991, p. 275-312. | MR 1084331 | Zbl 0688.60062

[12] L.D. Pitt, Positively Correlated Normal Variables are Associated, Ann. of Prob., vol. 10, 1982, p. 496-499. | MR 665603 | Zbl 0482.62046

[13] R.S. Ellis et C.M. Newman, Necessary and Sufficient Conditions for the GHS Inequality with Applications to Analysis and Probability, Trans. Am. Math. Soc., 1978, p. 237. | MR 492131 | Zbl 0412.35084

[14] M.L. Eaton, Lectures on Topics in Probability Inequalities, CWI Tract. Centrum voor Wiskunde in Informatica, 1987. | MR 889671 | Zbl 0622.60024

[15] J.D. Esary, F. Proschan et D.W. Walkup, Association of Random Variables with Applications, Ann. Math. Stat., vol. 38, 1967, p. 1466-1474. | MR 217826 | Zbl 0183.21502