The results of this thesis are organized in three parts that are nearly independent. In the first part, we treat the problem of the defintion of a class of Markov processes with infinitely many coordinates, namely interacting particle systems. We propose a construction involving neither functional analysis, nor martingale problems. This is done using elementary probabilistic tools, such as proper couplings. Our technique requires a certain assumption on the jump rates which is, up to a slight generalization, the one used in T. M. Liggett's construction. Our construction has the advantage to give more intuition on the necessity of this assumption. In the second part, we consider a crystal growth model proposed by D. J. Gates and M. Westcott in 1987, where floating particles are packed on the surface of a square-lattice crystal, with prescribed deposition rates. We treat the question of the recurrence and positive recurrence of the interface, according to the value of certain parameters. We study especially a zone of parameters where transience and positive recurrence coexist. In this zone a critical phenomenon is suspected to occur. The third part deals with the question of the convergence in law for the subcritical contact process (on Z) seen from the edge, starting from a half-line of occupied sites. First we give an alternative proof of a recent result by E. D. Andjel, stating that convergence holds in a closely related discrete-time model. In continuous time we establish that the finite contact process seen from the edge has a Yaglom limit.
