Speed processes for the Totally asymmetric exclusion and zero-range processes

Exclusion process and the Zero-range process are two important examples of particle systems on Z that gathered a lot of attention in  statistical physics. In this talk I will focus on the totally asymmetric exclusion process and the constant-rate totally asymmetric zero-range process. I will define the two models and discuss  their basic properties such as their density evolution and stationary measures. We will then introduce multi-type version of these processes (where particles of several types walk on Z according to the dynamics of the model, with lower type particles having priority over higher type ones) and study initial conditions in when a 2nd class particle develops a random  asymptotic speed. We will use these to define new "speed processes" and develop some of their properties. An important tool is an extension of a classic bijection between these two models to their multi-type version which allows translation of results between the two models.

The talk is based on joint work with O. Angel and B. Valko (TASEP) and current work in progress with P. Goncalves and J. Martin.