Ergodicity of Spitzer's renewal model

Vladas Sidoravicius and Maria Eulália Vares

Stochastic Processes and their Applications, 1995, vol. 55, issue 1, 119-130

Abstract: Answering a question raised in Andjel and Vares (1992), we prove the ergodicity of the infinite-dimensional renewal process whose coordinates are indexed by d 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 d. This also yields uniqueness of Gibbs measures.

Keywords: Multi-dimensional; renewal; process; Ergodicity; Attractiveness; Absence; of; phase; transition (search for similar items in EconPapers)
Date: 1995
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