Ergodicity of Spitzerʹs renewal model

Answering a question raised in Andjel and Vares (1992), we prove the ergodicity of the infinite-dimensional renewal process whose coordinates are indexed by Zd and whose failure rate at any given site is the average of the ages of its neighbors plus a positive constant c, for any d ≥ 1, c > 0. The main point is to prove the convergence of zero boundary Gibbs measures as the volume tends to Zd. This also yields uniqueness of Gibbs measures.