Metastabilty and Condensation for Zero Range Processes

vendredi 11 octobre 2019, 9h30 - 10h30

A central task of statistical mechanics is to explain the macroscopic behavior of a phenomenon in terms of its microscopic details. In this talk I will discuss the macroscopic evolution for a family of toy models that has been designed to understand and analyze the phenomena of metastability and condensation. These toy models are examples of stochastic particle systems known as Zero Range Processes. They are particularly tractable mathematically because of their simple interaction mechanism, and explicit equilibrium states. As the number of particles $N$, and the number sites $L$ increase to infinity with $N/L>\rho_c$, for a suitable critical density $\rho_c$, then most the time, the particles tend to condense at a unique random site. After a suitable rescaling of time, the location of the condensate would follow a macroscopic evolution that is given by a L\’evy process associated with a L\’evy measure that can be described explicitly in terms of the microscopic details of the underlying ZRP.