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Levi Haunschmid-Sibitz: The stochastic six-vertex model speed process

Date: 2024-12-11

Time: 14:00 - 15:00

Speaker
Levi Haunschmid-Sibitz, KTH Royal Institut of Technology

Abstract
We study the stochastic six vertex model with step initial conditions on the quadrant. Putting a single second-class particle at the origin, we show that the speed of this second-class particle converges almost surely. This allows one to define the stochastic-six vertex model speed process. To prove this result we develop tail bounds in the moderate devaitions regime for the height function of the stochastic six vertex model by using connections to determinantal point processes. We also need and prove a novel result which states that a second-class particle is overtaken by at most a geometric number of third-class particles. In this talk, after introducing the model, I will sketch the main proof and try to explain the tools that go into proving. Afterwards, I will explain some of the main properties of the stochastic six-vertex model speed process and how it is connected to the ASEP speed process.