Department of Mathematics

Indian Institute of Science

Bangalore 560 012

 

SEMINAR

 

Speaker

:

Sourav Sarkar 
Affiliation : UC Berkeley

Subject Area

:

Mathematics

 

Venue

:

Department of Mathematics, Lecture Hall I

 

Time

:

03:00 - 04:00 p.m.

 

Date  

:

January 11, 2017 (Wednesday)

Title

:

"Limiting measure for TASEP with a slow bond"
Abstract

:

It was shown by Basu, Sidoravicius and Sly that a TASEP starting with the step initial condition, i.e., with one particle each at every nonpositive site of Z and no particle at positive sites, with a slow bond at the origin where a particle jumping from the origin jumps at a smaller rate r < 1, has an asympototic current which is strictly less than 1/4. Here we study the limiting measure of the TASEP with a slow bond. The distribution of regular TASEP started with the step initial condition converges to the invariant product Bernoulli measure with density 1/2 . The slowdown due to the slow bond implies that there is a long range e?ect near the origin where the region to the right of origin is sparser and there is a tra?c jam to the left of the slow bond with particle density higher than a half. However, the distribution becomes close to a product Bernoulli measure as one moves far away from the origin, albeit with a di?erent density ? < 1/2 to the right of the origin and ?' > 1/2 to the left of the origin. This answers a question due to Liggett. The proof uses the correspondence between TASEP and directed last passage percolation on Z^2 with exponential passage times, and the geometric properties of the maximal paths there.