Boundary current fluctuations for the half space ASEP

04/26/2023 3:30 pm - 4:30 pm
Benjamin McKenna Changji Xu
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Probability Seminar

Speaker: Jimmy He (MIT)

Title: Boundary current fluctuations for the half space ASEP

Abstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.