Event № 666
Event № 666
TE Seminar in Probability and Stochastic Processes - Gidi Amir 12/11/2013, Tuesday, 11:30
Name: Seminar in Probability and Stochastic Processes
Title: The speed process of the Totally Asymmetric Zero-Range Processes.
Speaker: Gidi Amir
Place: EE 861, Technion
Abstract: Exclusion processes and Zero-range processes 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 (TASEP) and the constant-rate totally asymmetric zero-range process (TAZRP). I will define the two models and discuss their basic properties such as their 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). In a paper with Angel and Valko, results on multi-type stationary measures for the TASEP and about the (random) speed of a second class particle in the "step" initial condition were used to define a speed process for the TASEP which turned out to have many interesting properties. I will briefly survey some results concerning that process, and then go on to describe a new speed process for the TAZRP. We will show how to generalize the multi-type "step" initial condition to the Zero-Range process and how to define a bijection between the models that allows to transfer some results in 2nd class particles to the TAZRP. We will then use these to define a speed process and analyze it. An important step is finding the stationary measures for the multi-type TAZRP, which will be analyzed as a system of queues in tandem. We will also show how to use the speed process to make simple calculations of the speed of a 2nd class particle in the rarefacation fan for TAZRP under certain initial conditions.
SubmittedBy: nick crawford , firstname.lastname@example.org
EventLink: Event № 666