2026 Theses Doctoral

Boundary interactions for models in the KPZ universality class

Yang, Zongrui

The KPZ universality class, introduced in 1986 by Kardar, Parisi, and Zhang [1], encompasses a wide range of probabilistic models. Boundary interactions in such systems often lead to new and rich algebraic, probabilistic, and physical phenomena.

This thesis collects eleven works on boundary-driven models in the KPZ universality class carried out during my PhD studies at Columbia University. These results contribute to the understanding of stationary measures for processes that interact with boundaries and to the construction of universal limiting objects (Gibbsian line ensembles) in half-space regimes.

The models studied include the asymmetric simple exclusion process (ASEP), stochastic six-vertex models and their higher-spin generalizations, geometric last-passage percolation and log-gamma polymer models, all with open boundaries, as well as models arising as their scaling limits, including the open KPZ equation, the open KPZ fixed point, and the half-space Airy line ensemble.