×

Limit theorems for sums of dependent random variables occurring in statistical mechanics. (English) Zbl 0364.60120


MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bleher, P.M., Sinai, Y.G.: Critical indices for Dyson’s asymptotically hierarchical models. Commun. Math. Phys. 45, 247-278 (1975)
[2] Blume, M., Emery, V.J., Griffiths, R.B.: Ising model for the ? transition and phase separation in He3-He4 mixtures. Phys. Rev. A4, 1071-1077 (1971)
[3] Brout, R.H.: Phase transitions. In: Statistical Physics: Phase Transitions and Superfluidity (Chretien M.; Gross E.P.; Deser S.; eds.). New York: Gordon and Breach, 1968
[4] Collet, P., Eckmann, J.-P.: The ?-expansion for the hierarchical model. Univ. de Genève (preprint) (1977)
[5] Dunlop, F., Newman, C.M.: Multicomponent field theories and classical rotators. Commun. math. Phys. 44, 223-235 (1975)
[6] Ellis, R.S., Monroe, J.L., Newman, C.M.: The GHS and other correlation inequalities for a class of even ferromagnets. Commun. Math. Phys. 46, 167-182 (1976)
[7] Ellis, R.S., Newman, C.M.: Fluctuationes in Curie-Weiss Exemplis. In: Proceedings of the International Conference on the Mathematical Problems in Theoretical Physics, Rome, 1977
[8] Ellis, R.S., Newman, C.M.: Necessary and sufficient conditions for the GHS inequality with applications to probability and analysis. Trans. Amer. Math. Soc. 237, 83-99 (1978) · Zbl 0412.35084
[9] Feller, W.: An introduction to probability theory and its applications. Vol.11. New York: Wiley 1966 · Zbl 0138.10207
[10] Gallavotti, G., Jona-Lasinio, G.: Limit theorems for multi-dimensional Markov processes. Commun. math. Phys. 41, 301-307 (1975) · Zbl 0343.60043
[11] Ghizzetti, A., Ossicini, A.: Quadrature formulae. New York: Academic, 1970 · Zbl 0194.36901
[12] Glimm, J., Jaffe, A.: A tutorial course in constructive field theory. Proceedings of the 1976 Cargèse summer school. · Zbl 0574.01019
[13] Griffiths, R.B., Hurst, C.A., Sherman, S.: Concavity of magnetization of an Ising ferromagnet in a positive external field. J. Math. Phys. 11, 790-795 (1970)
[14] Kac, M.: Mathematical mechanisms of phase transitions. In: Statistical Physics: Phase Transitions and Superfluidity (Chretien, M.; Gross, E.P.; Deser, S.; eds.). New York: Gordon and Breach, 1968 · Zbl 0162.29301
[15] Kadanoff, L.P.: Scaling, universality, and operator algebras. In: Phase transitions and critical phenomena, Vol. 5 A, pp. 1-34 (Domb, C.; Green, M.S.; eds.). New York: Academic, 1976
[16] Karlin, S., Studden, W.J.: Tchebycheff systems: with applications in analysis and statistics. New York: Interscience, 1966 · Zbl 0153.38902
[17] Mandelbrot, B.: Limit theorems on the self-normalized range for weakly and strongly dependent processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 31, 271-285 (1975) · Zbl 0288.60033
[18] Molcanov, S.A., Sudarev, Ju. N.: Gibbs states in the spherical model. Soviet Math. Dokl. 16, 1254-1257 (1975) · Zbl 0339.60089
[19] Richter, V.: Multidimensional local limit theorems for large deviations. Theor. Probability Appl. 3, 100-106 (1958)
[20] Shohat, J.A., Tamarkin, J.D.: The problem of moments. New York: Amer. Math. Soc. 1943 · Zbl 0063.06973
[21] Simon, B., Griffiths, R.B.: The (?) 2 4 field theory as a classical Ising model. Commun. math. Phys. 33, 145-164 (1973)
[22] Stanley, H.E.: Introduction to phase transitions and critical phenomena. New York: Oxford, 1971
[23] Stroud, A.H.: Numerical quadrature and solution of ordinary differential equations. Berlin-Heidelberg-New York: Springer, 1974 · Zbl 0298.65018
[24] Stroud, A.H., Secrest, D.: Approximate integration formulae for certain spherically symmetric regions. Math. Comput. 17, 105-135 (1963) · Zbl 0112.35302
[25] Taqqu, M.: Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheorie verw. Gebiete 31, 287-302 (1975) · Zbl 0303.60033
[26] Thompson, C.: Mathematical statistical mechanics. New York: Macmillan, 1972 · Zbl 0244.60082
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.