Last Passage percolation: modulus of continuity and the slow bond problem

Seminar | May 8 | 3-4 p.m. | 1011 Evans Hall

 Sourav Sarkar, UC Berkeley

 Department of Statistics

The talk has two parts. In the first part we will speak on the modulus of
continuity in Poissonian last passage percolation, a model lying in the
KPZ universality class. In the second part we speak on the “slow bond”
model, where Totally Asymmetric Simple Exclusion Process (TASEP) on
$\mathbb{Z}$ (a model which can be thought to simulate a one-way traffic
movement) is modified by adding a slow bond at the origin, that is, particles
at the origin wait longer before making jumps. A conjectural description
of properties of invariant measures of TASEP with a slow bond at the
origin was provided in Liggett's 1999 book . We establish Liggett’s
conjectures and in particular show that TASEP with a slow bond at the
origin, starting from step initial condition, converges in law to an
invariant measure that is asymptotically close to product measures with
different densities far away from the origin towards left and right. Joint work with Alan Hammond, Allan Sly and Riddhipratim Basu.