Metastability of Zero Range Processes

This dissertation is about the metastability of a condensed zero range process on a fixed finite set. Most of the time, nearly all particles of this zero range process are at one single site. The site of condensate asymptotically behaves as a Markov chain. This is proven for the reversible case, for the totally asymmetric case, and for the non-reversible case using the martingale approach which requires precise estimates of capacities. We prove the metastability of zero range processes on a fixed finite set with an approach using solutions of Poisson equations. By this approach, we circumvent precise estimates of capacities and prove the metastability for both reversible and non-reversible cases