Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
PAUL CHLEBOUN (Warwick University)
We discuss a general approach to understand phase separation and metastability in stochastic particle systems that exhibit a condensation transition. Condensation occurs when, above some critical density, a finite fraction of all the particles in the system accumulate on a single lattice site. We present a detailed analysis of a particular size-dependent zero-range process which was introduced as a toy model for clustering in granular media. This model also captures all the relevant details of more generic condensing zero-range processes close to the critical point. Results on the equivalence of ensembles and metastability are based on large deviation principles for the maximum of triangular arrays of independent random variables conditioned on their sum. We derive the saddle point structure of the associated free energy landscape, which implies different mechanisms for the dynamics of the condensate depending on the system parameters. These results lead us to an interesting conjecture on the stationary dynamics of the condensate in the thermodynamic limit.