The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

    Antal, Peter; Pisztora, Agoston. On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996), no. 2, 1036--1048. MR1404543 (98b:60168)

    Bricmont, Jean; Lebowitz, Joel L.; Maes, Christian. Percolation in strongly correlated systems: the massless Gaussian field. J. Statist. Phys. 48 (1987), no. 5-6, 1249--1268. MR0914444 (89c:82040)

    Cassandro, M.; Olivieri, E.; Pellegrinotti, A.; Presutti, E. Existence and uniqueness of DLR measures for unbounded spin systems. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 41 (1977/78), no. 4, 313--334. MR0471115 (57 #10854)

    Dieudonné, Jean. Calcul infinitésimal. (French) Hermann, Paris 1968 479 pp. (loose errata). MR0226971 (37 #2557)

    Dobrushin, R. L. Gaussian random fields---Gibbsian point of view. Multicomponent random systems, pp. 119--151, Adv. Probab. Related Topics, 6, Dekker, New York, 1980. MR0599534 (82d:60095)

    Doss, H.; Royer, G. Processus de diffusion associé aux mesures de Gibbs sur $ Rsp{ Zsp{ d}}$. (French) Z. Wahrsch. Verw. Gebiete 46 (1978/79), no. 1, 107--124. MR0512335 (80h:60122)

    Garet, Olivier. Gibbsian fields associated to exponentially decreasing quadratic potentials. Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), no. 3, 387--415. MR1689890 (2000g:60156)

    Garet, Olivier ; Marchand, RÈgine. Asymptotic shape for the chemical distance and first-passage percolation in random environment. Preprint. 2003. Available at ArXiv

    Georgii, Hans-Otto. Gibbs measures and phase transitions. de Gruyter Studies in Mathematics, 9. Walter de Gruyter & Co., Berlin, 1988. xiv+525 pp. ISBN: 0-89925-462-4 MR0956646 (89k:82010)

    Georgii, Hans-Otto; Häggström, Olle; Maes, Christian. The random geometry of equilibrium phases. Phase transitions and critical phenomena, Vol. 18, 1--142, Phase Transit. Crit. Phenom., 18, Academic Press, San Diego, CA, 2001. MR2014387

    Künsch, H. Gaussian Markov random fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 26 (1979), no. 1, 53--73. MR0539773 (81g:60056)

    Künsch, H. Reellwertige Zufallsfelder auf einem Gitter: Interpolationsprobleme, Variationsprinzip und statistische Analyse. PhD thesis, Z¸rich, 1980.

    Liggett, T. M.; Schonmann, R. H.; Stacey, A. M. Domination by product measures. Ann. Probab. 25 (1997), no. 1, 71--95. MR1428500 (98f:60095)

    Molchanov, S. A.; Stepanov, A. K. Percolation in random fields. I. (Russian) Teoret. Mat. Fiz. 55 (1983), no. 2, 246--256. MR0734878 (85j:60091)

    Molchanov, S. A.; Stepanov, A. K. Percolation in random fields. II. (Russian) Teoret. Mat. Fiz. 55 (1983), no. 3, 419--430. MR0711007 (85j:60092)

    Molchanov, S. A.; Stepanov, A. K. Percolation in random fields. III. (Russian) Teoret. Mat. Fiz. 67 (1986), no. 2, 177--185. MR0851557 (87m:60117)

    Newman, Charles M. A surface view of first-passage percolation. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 1017--1023, Birkhäuser, Basel, 1995. MR1404001 (97h:60127)

    Roberts, A.P. ; Knackstedt, M.A. Structure-property correlations in model composite materials. Phys. Rev. E, 54:2313--2328, september 1996.

    Roberts, A.P. ; Teubner, M. Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation. Phys. Rev. E, 51:4141--4154, may 1995.

    Rudin, Walter. Function theory in the unit ball of $ Csp{n}$. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], 241. Springer-Verlag, New York-Berlin, 1980. xiii+436 pp. ISBN: 0-387-90514-6 MR0601594 (82i:32002)

    Russo, Lucio. An approximate zero-one law. Z. Wahrsch. Verw. Gebiete 61 (1982), no. 1, 129--139. MR0671248 (84e:60153)

    Sinai, Ya. G. Introduction to ergodic theory. Translated by V. Scheffer. Mathematical Notes, 18. Princeton University Press, Princeton, N.J., 1976. 144 pp. ISBN: 0-691-08182-4 MR0584788 (58 #28437)

    Spitzer, Frank. Principles of random walk. The University Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London 1964 xi+406 pp. MR0171290 (30 #1521)

    van Beijeren, Henk; Sylvester, Garrett S. Phase transitions for continuous-spin Ising ferromagnets. J. Functional Analysis 28 (1978), no. 2, 145--167. MR0484201 (58 #4128)

    Watson, G. N. A treatise on the theory of Bessel functions. Reprint of the second (1944) edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1995. viii+804 pp. ISBN: 0-521-48391-3 MR1349110 (96i:33010)



Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.