×

zbMATH — the first resource for mathematics

Limit theorems for sums of dependent random variables occurring in statistical mechanics. II: Conditioning, multiple phases, and metastability. (English) Zbl 0404.60096

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
60G50 Sums of independent random variables; random walks
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brout, R.H.: Phase transitions. In: Statistical Physics: Phase Transitions and Superfluidity, 3-103. Edited by M. Chretien, E.P. Gross, and S. Deser. New York: Gordon and Breach 1968
[2] Chung, K.L.: A Course in Probability Theory (Second Edition). New York: Academic Press 1974 · Zbl 0345.60003
[3] Ellis, R.S.: The Legendre transformation and concepts of entropy. U. Mass. preprint (1978)
[4] Ellis, R.S., Newman, C.M.: Limit theorems for sums of dependent random variables occurring in statistical mechanics. Z. f. Wahrscheinlichkeitstheorie verw. Gebiete 44, 117-139 (1978) · Zbl 0364.60120 · doi:10.1007/BF00533049
[5] 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
[6] 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) · doi:10.1063/1.1665211
[7] Huang, K.: Statistical Mechanics. New York: John Wiley and Sons 1963
[8] Kac, M.: Mathematical mechanisms of phase transitions. In: Statistical Physics: Phase Transitions and Superfluidity, 241-305. Edited by M. Chretien, E.P. Gross, and S. Deser. New York: Gordon and Breach 1968
[9] Penrose, O., Lebowitz, J.L.: Rigorous treatment of metastable states in the van der Waals-Maxwell theory. J. Statist. Phys. 3, 211-236 (1971) · Zbl 0938.82521 · doi:10.1007/BF01019851
[10] Penrose, O., Lebowitz, J.L.: Toward a rigorous molecular theory of metastability. In: Fluctuation Phenomena. Studies in Statistical Mechanics. Edited by J.L. Lebowitz and E. W. Montroll. Amsterdam: North Holland
[11] Stanley, H.E.: Introduction to Phase Transitions and Critical Phenomena. New York: Oxford Univ. Press 1971
[12] Thompson, C.J.: 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.