"Large Deviations and Metastability" Enzo Olivieri, Maria Eulália Vares p. 26, line 5. Replace "x ∈ M " by "x ∈ M such that I(x) < +∞" p. 57, display (1.95). There is a redundant condition. Since ν and η are probability

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Abstract. We consider the symmetric simple exclusion process in the interval [−N, N ] with additional birth and death processes respectively on (N −K, N ], K > 0, and [−N, −N + K). The exclusion is speeded up by a factor N 2 , births and deaths by a factor N . Assuming propagation of chaos (a property proved in a companion paper, [3]) we prove convergence in the limit N → ∞ to the linear heat equation with Dirichlet condition on the boundaries; the boundary conditions however are not known a priori, they are obtained by solving a non linear equation. The model simulates mass transport with current reservoirs at the boundaries and the Fourier law is proved to hold.

We consider the stirring process in the interval Lambda(N) : = [-N; N] of Z with births and deaths taking place in the intervals I+ : = ( N K; N], and respectively I- : = [-N; -N + K), 1 <= K < N. We prove bounds on the truncated moments uniform in N which yield strong factorization properties