Calcul pseudodifférentiel en grande dimension et limites thermodynamiques

If P_n(h) is a h-pseudodifferential operator in $\text{R}{}^{\mathrm{n}}$ associated to an holomorphic semi-bounded symbol in some neighborhood of the real phase space, with bounded derivatives, we describe the symbol of e^?tP_n(h), by inegalities where the constants depend on the bounds for the derivatives of the symbol of P_n(h), but not on the dimension n. Some applications to thermodynamic limits are given. To cite this article: C. Royer, C. R. Acad. Sci. Paris, Ser. I 336 (2003).