Mixing times for coagulation-fragmentation processes

There is a substantial literature on reversible Markov models for Coagulation and Fragmentation of finite sets - see e.g. Durrett-Granovsky-Gueron (1999). But is is a (broad and vague) Open Problem to relate this to the "Markov Chain Mixing Times" literature, specifically to get bounds on relaxation/mixing times in terms of the model parameters. Here are brief notes from an unposted section of Aldous-Fill RWG on one model. Another natural model is the finite analog of the split-merge transformation model in P Diaconis, E Mayer-Wolf, O Zeitouni (2003).

Update (February 2018). References to more recent literature are in this 2016 Hingant-Yvinec preprint.

History. First written here August 2012, but mentioned in conversation many years earlier.