Guillaume Barraquand (Columbia University)
Wed, Jan 20, 11:00am, Aud

We will consider exclusion processes on the one-dimensional integer lattice, starting from a densely packed configuration (step initial condition). We address the non-universal behaviour of the first particle. We will review some known results (TASEP, ASEP), and then focus on two different dynamics.

The multi-particle asymmetric diffusion model, a Bethe ansatz solvable process introduced by Sasamoto and Wadati. For these dynamics, the first particle fluctuates on the t^{1/3} scale with Tracy-Widom GUE fluctuations.

The Facilitated TASEP, an exclusion process where each particle jumps to the right by one at rate 1 only when the right neighbouring site is empty, and the left neighbouring site is occupied. For these dynamics, the first particle fluctuates on the t^{1/3} scale with — surprinsingly —Tracy-Widom GSE fluctuations.

In the latter case, we will sketch the main lines of our proofs. The exact solvability comes from a coupling with a model of Last Passage Percolation on a half-quadrant, that we analyse using the formalism of Pfaffian Schur processes. Joint works with Jinho Baik, Ivan Corwin and Toufic Suidan.

Guillaume Barraquand (Columbia University)Wed, Jan 20, 11:00am, Aud

We will consider exclusion processes on the one-dimensional integer lattice, starting from a densely packed configuration (step initial condition). We address the non-universal behaviour of the first particle. We will review some known results (TASEP, ASEP), and then focus on two different dynamics.

- The multi-particle asymmetric diffusion model, a Bethe ansatz solvable process introduced by Sasamoto and Wadati. For these dynamics, the first particle fluctuates on the t^{1/3} scale with Tracy-Widom GUE fluctuations.
- The Facilitated TASEP, an exclusion process where each particle jumps to the right by one at rate 1 only when the right neighbouring site is empty, and the left neighbouring site is occupied. For these dynamics, the first particle fluctuates on the t^{1/3} scale with — surprinsingly —Tracy-Widom GSE fluctuations.

In the latter case, we will sketch the main lines of our proofs. The exact solvability comes from a coupling with a model of Last Passage Percolation on a half-quadrant, that we analyse using the formalism of Pfaffian Schur processes. Joint works with Jinho Baik, Ivan Corwin and Toufic Suidan.