E. Effet, 11 est encore vrai; on en donnera l'´ enoncé précis et la preuve dans le Théorème 5.16. Par contre les techniques que nous développons ici pour d ? 3 ne permettent pas de démontrer le lemme 4.8 dans le cas d = 4, et donc on ne peut pas cerner quand l'hypothèse d'existence de moments pour la variable ? ? , dans la partie réciproque du Théorème 5.16, est satisfaite. De même, la démonstration de la Proposition 5

]. S. Bibliographie1, Y. G. Albeverio, M. Kondratiev, and . Röckner, Analysis and geometry on configuration spaces : The Gibbsian case, J. Funct. Anal, vol.157, pp.242-291, 1998.

S. Albeverio, M. Röckner, and T. S. Zhang, Markov uniqueness for a class of infinite dimensional Dirichlet operators, Stochastic Processes and Optimal Control, Stochastics Monographs, vol.7, pp.1-26, 1993.

P. Cattiaux, S. Roelly, and H. Zessin, Une approche gibbsienne des diffusions browniennes infini-dimensionnelles, Probab. Theory. Rel, pp.223-248, 1996.

. Ph, P. Courrège, and . Renouard, Oscillateurs anharmoniques, mesures quasi-invariantes sur C(R,R) et théorie quantique des champs en dimension 1, astérisque 22-23 Soc, 1975.

P. Dai-pra and S. Roelly, An existence result for infinite-dimensional Brownian diffusions with non-regular and non-Markovian drift, 2002.

P. Dai-pra, S. Roelly, and H. Zessin, A Gibbs variational principle in space-time for infinite-dimensional diffusions, Probability Theory and Related Fields, vol.122, issue.2, pp.289-315, 2002.
DOI : 10.1007/s004400100170

D. Dereudre, Une caract??risation de champs de Gibbs canoniques sur et, Comptes Rendus Mathematique, vol.335, issue.2, pp.177-182, 2002.
DOI : 10.1016/S1631-073X(02)02452-4

D. Dereudre, Interacting Brownian particles and Gibbs fields on pathspaces , soumis pour publication en, 2002.

D. Dereudre, Deux caractérisations de mélanges de processus ponctuels de Poisson, 1999.

J. Deuschel, Infinite dimensional diffusion processes as Gibbs measures on C[0,1] Z d , Probab. Theory Rel, pp.325-340, 1987.

R. L. Dobrushin, Investigation of the conditions of the Asymptotic Existence of the configuration Integral of the Gibbs distribution, Teorija verojatn. i ee Prim, pp.626-643, 1964.

R. L. Dobrushin and J. Fritz, Non-equilibrium dynamics of onedimensional infinite particle systems with a hard-core interaction, Comm. Math. Phys, pp.55-275, 1977.

J. Fritz and R. L. Dobrushin, Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction, Communications In Mathematical Physics, vol.9, issue.1, pp.67-81, 1977.
DOI : 10.1007/BF01651694

M. E. Fisher and D. Ruelle, The Stability of Many???Particle Systems, Journal of Mathematical Physics, vol.7, issue.2, pp.260-270, 1966.
DOI : 10.1063/1.1704928

M. Fradon, S. Roelly, and H. Tanemura, An infinite system of Brownian balls with infinite range interaction, Stochastic Process, Appl, pp.90-91, 2000.

J. Fritz, Gradient Dynamics of Infinite Point Systems, The Annals of Probability, vol.15, issue.2, pp.487-514, 1987.
DOI : 10.1214/aop/1176992156

J. Fritz, S. Roelly, and H. Zessin, Stationary states of interacting Brownian motions, Stud. Sci. Math. Hung, vol.34, pp.151-164, 1998.

H. Föllmer, Time reversal on Wiener space, Lecture Notes in Mathematics, vol.1059, issue.4, pp.117-129, 1986.
DOI : 10.1007/BFb0100047

H. Föllmer and A. Wakolbinger, Time reversal of infinite-dimensional diffusions, Stochastic Process, Appl, vol.22, pp.59-77, 1986.

B. Gaveau and P. Trauber, L'int??grale stochastique comme op??rateur de divergence dans l'espace fonctionnel, Journal of Functional Analysis, vol.46, issue.2, pp.230-238, 1982.
DOI : 10.1016/0022-1236(82)90036-2

H. Georgii, Canonical Gibbs measures, Lecture Notes in Math, vol.760, 1979.
DOI : 10.1007/BFb0068557

H. Georgii, Equilibria for particle motions : Conditionally balanced point random fields, Exchangeability in Probability and Statistics, pp.265-280, 1982.

H. Georgii, Gibbs measures and phase transitions, 1988.

E. Glötzl, O. K. Bemerkungen-zu-einer-arbeit-von, and . Kozlov, Bemerkungen zu einer Arbeit von O. K. Kozlov, Mathematische Nachrichten, vol.33, issue.1, pp.277-289, 1980.
DOI : 10.1002/mana.19800940116

S. Goldstein, R. Kuik, J. L. Lebowitz, and . Ch, Maes, From PCA's to equilibrium systems and back, Comm. Math. Phys, pp.125-128, 1989.

J. Jacod, Calcul Stochastique etprobì emes de martingales, Lectures Notes in Math, 1979.

O. K. Kozlov, Gibbsian description of point random fields, Theory Probab, Appl, vol.21, pp.339-356, 1976.

A. N. Kolmogorov, Zur Umkehrbarkeit der statistischen Naturgesetze, Zur Umkehrbarkeit der statistischen Naturgesetze, pp.766-772, 1937.
DOI : 10.1007/BF01571664

R. Lang, Unendlich-dimensionale Wienerprozesse mit Wechselwirkung, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.24, issue.66, pp.55-72, 1977.
DOI : 10.1007/BF00534170

R. Lang and I. Unendlich-dimensionale-wienerprozesse-mit-wechselwirkung, Unendlich-dimensionale Wienerprozesse mit Wechselwirkung, Zeitschrift f??r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.18, issue.4, pp.277-299, 1977.
DOI : 10.1007/BF01877496

J. L. Lebowitz, A. E. Mazel, and E. Presutti, Rigorous proof of liquidvapour phase transition in a continuum particle system, Phys. Rev. Letters, pp.80-4701, 1998.

J. Mecke, A characterization of Mixed Poisson Processes, Rev. Roum. Math. Pures et Appl, vol.21, pp.1355-1360, 1976.

A. Millet, D. Nualart, and M. Sanz, Time reversal for infinite-dimensional diffusions, Probability Theory and Related Fields, vol.3, issue.3, pp.315-347, 1989.
DOI : 10.1007/BF00339991

R. A. Minlos, Introduction to mathematical statistical physics, 2000.
DOI : 10.1090/ulect/019

R. A. Minlos, S. Roelly, and H. Zessin, Gibbs states on space-time, Potential Analysis, vol.13, issue.4, pp.367-408, 2000.
DOI : 10.1023/A:1026420322268

X. X. Nguyen and H. Zessin, Integral and differential characterizations of the Gibbs process, Math. Nachr, vol.88, pp.105-115, 1979.

D. Nualart, The Malliavin calculus and related topics , Probability and its Applications, 1995.

. Ch and . Preston, Random fields, Lecture Notes in Math, 1976.

N. Privault, A characterization of grand canonical Gibbs measures by duality, Potential Analysis 15, pp.23-28, 2001.

P. N. Pusey, Langevin approach to the dynamics of interacting Brownian particles, J. phys, pp.15-1291, 1982.

B. Rauchenschwandtner and A. Wakolbinger, Some aspects of the Papangelou kernel, Colloquia mathematica societatis Janos Bolyai, Hungary, vol.24, pp.325-336, 1978.

S. Roelly and H. Zessin, Une caractérisation des mesures de Gibbs sur C(0,1) Z d par le calcul des variations stochastiques, Ann. Inst. H. Poincaré, vol.29, issue.3, pp.327-338, 1993.

S. Roelly and H. Zessin, Une caractérisation de champs gibbsiens sur un espace de trajectoires, C.R. Acad. Sci. Paris, Ser. I, vol.321, pp.1377-1382, 1995.

G. Royer and M. Yor, Représentation intégrale de certaines mesures quasiinvariantes sur C(R); mesures extrémales et propriété de Markov, Ann. Inst. Fourier (Grenoble), pp.26-28, 1976.

D. Ruelle and S. Mechanics, Rigorous Results, 1969.

D. Ruelle, Superstable interactions in classical statistical mechanics, Communications in Mathematical Physics, vol.87, issue.2, pp.127-159, 1970.
DOI : 10.1007/BF01646091

F. L. Spitzer, Markov Random Fields and Gibbs Ensembles, The American Mathematical Monthly, vol.78, issue.2, pp.142-154, 1971.
DOI : 10.2307/2317621

H. Spohn, Equilibrium fluctuations for interacting Brownian particles, Communications In Mathematical Physics, vol.34, issue.1, pp.1-33, 1986.
DOI : 10.1007/BF01464280

C. J. Thompson, Mathematical Statistical Mechanics, 1972.
DOI : 10.1515/9781400868681

A. Wakolbinger and G. Eder, A condition ? c ? for Point Processes

M. Yoshida, Construction of infinite dimensional interacting diffusion processes through Dirichlet forms, Probability Theory and Related Fields, vol.106, issue.2, pp.265-297, 1996.
DOI : 10.1007/s004400050065