HOROWITZ SEMINAR

PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS

Gidi Amir (U. of Toronto)

will speak on

The speed process of the Totally Asymmetric Exclusion Process (TASEP)

ABSTRACT:This is joint work with Omer Angel and Benedek Valko.

We study an exclusion process on Z where each particle is assigned a class (number in Z) and each particle tries to swap places with its right neighbor with rate 1 if that neighbor has a higher class number.
(Alternatively, each edge of Z is "sorted" with rate 1)

With the right starting conditions, the position of each particle (normalized by the time) converges to a constant speed.
The speed of each particle is uniform in [-1,1], but there are strong dependencies between the behavior of different particles.

We study this exclusion process and the distribution of its related speed process.
We show a new symmetry for the multi-type TASEP, and prove that the joint distribution of the speeds is stationary with respect to the multi-type TASEP dynamics (where the speeds are considered as the classes of the particles).
This allows us to utilize known results on stationary measure for the multi-type TASEP to deduce various marginals of the speed process such as the joint distribution of the speeds for 3 consequent particles .
Another surprising consequence is the existence of infinite "convoys" – particles (with different classes) all converging to the same speed. Some of our results apply also to the partially asymmetric case as well.

No prior knowledge on exclusion processes is assumed, and all definitions will be given within the lecture.

To suggest a talk (yours, or someone elses), contact Jon. Aaronson: aaro at post dot tau dot ac dot il

Back to: Jon Aaronson's homepage.